1. Bounds on the game isolation number and exact values for paths and cyclesCsilla Bujtás, Tanja Dravec, Michael A. Henning, Sandi Klavžar, 2026, izvirni znanstveni članek Povzetek: The isolation game is played on a graph $G$ by two players who take turns playing a vertex such that if $X$ is the set of already played vertices, then a vertex can be selected only if it dominates a vertex from a nontrivial component of $G \setminus N_G[X]$, where $N_G[X]$ is the set of vertices in $X$ or adjacent to a vertex in $X$. Dominator wishes to finish the game with the minimum number of played vertices, while Staller has the opposite goal. The game isolation number $\iota_{\rm g}(G)$ is the number of moves in the Dominator-start game where both players play optimally. If Staller starts the game the invariant is denoted by $\iota_{\rm g}'(G)$. In this paper, $\iota_{\rm g}(C_n)$, $\iota_{\rm g}(P_n)$, $\iota_{\rm g}'(C_n)$, and $\iota_{\rm g}'(P_n)$ are determined for all $n$. It is proved that there are only two graphs that attain equality in the upper bound $\iota_{\rm g}(G) \le \frac{1}{2}|V(G)|$, and that there are precisely eleven graphs which attain equality in the upper bound $\iota_{\rm g}'(G) \le \frac{1}{2}|V(G)|$. For trees $T$ of order at least three it is proved that $\iota_{\rm g}(T) \le \frac{5}{11}|V(T)|$. A new infinite family of graphs $G$ is also constructed for which $\iota_{\rm g}(G) = \iota_{\rm g}'(G) = \frac{3}{7}|V(G)|$ holds.
Ključne besede: isolating set, isolation game, paths and cycles, trees
Objavljeno v DiRROS: 12.06.2026; Ogledov: 115; Prenosov: 94
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2. The exact region determined by Spearman’s footrule, Gini’s gamma and Kendall’s tauDamjana Kokol-Bukovšek, Petra Lazić, Blaž Mojškerc, Nik Stopar, 2026, izvirni znanstveni članek Povzetek: To quantify the degree of association between random variables, concordance measures are employed. To express such a degree, a single measure might give too much space, so several are used for comparison. In this paper we study the ternary relation between three well-known (weak) concordance measures, namely Blomqvist’s beta, Concordance measures are used to express the degree of association between random variables. Practitioners may use several distinct concordance measures to narrow down the space of possible dependence structures. Consequently, the relations between different (weak) concordance measures have been extensively studied in recent years. The goal of this paper is to study the relation between Kendall’s tau, Gini’s gamma and Spearman’s footrule. In particular, we describe the exact region determined by these three measures, using shuffles of M and ordinal sums of copulas. We also provide the formulas for five main (weak) concordance measures and Chatterjee’s xi of ordinal sums of copulas.
Ključne besede: copula, dependence concepts, supremum and infimum of a set of copulas, measures of concordance, quasi-copula, local bounds
Objavljeno v DiRROS: 08.04.2026; Ogledov: 205; Prenosov: 151
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3. Builder-Blocker mutual-visibility gameVesna Iršič Chenoweth, Sandi Klavžar, Gregor Rus, Elif Tan, Jing Tian, 2026, izvirni znanstveni članek Povzetek: This article discusses mutual-visibility in graphs through a game-based version of the problem. Two players, Builder and Blocker, alternately select an unmarked vertex on a graph keeping the property that the set of marked vertices forms a mutual-visibility set. The game ends when no such selection is possible. The goal of Builder is to create a largest possible mutual-visibility set, Blocker's goal is the opposite. The central problem here is to determine the number of vertices selected during the game assuming that both players played optimally. Bounds on this number are proved and several general properties of the game derived. Special attention is paid to complete multipartite graphs and Hamming graphs.
Ključne besede: mutual-visibility set, games on graphs, complete multipartite graph, Hamming graph
Objavljeno v DiRROS: 02.04.2026; Ogledov: 290; Prenosov: 201
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4. Transcriptome profiles of skeletal muscle in krškopolje and modern hybrid pigs : genotype comparison and effects of dietary protein reductionMilka Vrecl, Gregor Fazarinc, Malan Štrbenc, Klavdija Poklukar Žnidaršič, Marjeta Čandek-Potokar, Martin Škrlep, 2026, zaključena znanstvena zbirka raziskovalnih podatkov Povzetek: RNA sequencing was performed to compare two pig breeds (the Slovenian Krškopolje breed and a modern commercial breed) and to evaluate the effect of breed specific dietary protein reduction on the transcriptomic profiles of two skeletal muscles: longissimus thoracis et lumborum (LD) and semispinalis capitis (SSC). Differentially expressed genes (DEGs) were identified using the criteria |log2FC| > 1 and q value < 0.005. The effect of dietary protein reduction was minimal in both breeds and muscles, with only small numbers of DEGs detected. In Krškopolje pigs receiving medium protein (MP) or low protein (LP) diets, no DEGs were identified. In contrast, in the modern breed, 10 DEGs were detected when comparing the high protein (HP) with the MP diet group. A similar pattern was observed in SSC, where 19 DEGs were detected in Krškopolje pigs (MP vs. LP) and 16 DEGs in the modern breed (HP vs. LP). In comparison, when the LD and SSC transcriptome profiles of the modern breed were compared with those of the Krškopolje breed, the number of DEGs was substantially higher:149 in LD and 201 in SSC. The DEGs in LD of modern breed reflect a shift toward faster growing, more glycolytic muscle with distinct immune and neuromuscular regulation. Likewise, the SSC of modern breed shows stronger activation of growth related and metabolic signaling pathways.
Ključne besede: RNA sequences, pigs, adipose tissue, high throughput sequencing, RNA, transcriptome profiles, gene expression, locel breeds, hybrid breeds, data, data set
Objavljeno v DiRROS: 24.03.2026; Ogledov: 345; Prenosov: 69
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5. Maker-Breaker resolving game played on lexicographic products of graphsK. S. Savitha, Sandi Klavžar, Tijo James, 2026, izvirni znanstveni članek Povzetek: In the Maker-Breaker resolving game, two players named Resolver and Spoiler alternately select unplayed vertices of a given graph $G$. The aim of Resolver is to select all the vertices of some resolving set of $G$, while Spoiler aims to select at least one vertex from every resolving set of $G$. In this paper, this game is investigated on the lexicographic product of graphs. It is proved that if Spoiler has a winning strategy on a graph $H$ no matter who starts the game, or if the first player has a winning strategy on $H$, then Spoiler always has a winning strategy on $G\circ H$. Special attention is paid to lexicographic products in which the second factor is a complete graph, a path, or a cycle. For instance, in $G\circ P_{2\ell}$ and in $G\circ C_{2\ell}$, Resolver always wins, while in $G\circ P_{2\ell+1}$ and in $G\circ C_{2\ell+1}$ the same conclusion holds provided $G$ is free from false twins. On the other hand, Spoiler always wins on $G\circ P_5$. In most of the cases, the corresponding Maker-Breaker resolving number is also determined.
Ključne besede: Maker-Breaker game, metric dimension, resolving set, Maker-Breaker resolving game, lexicographic product of graphs
Objavljeno v DiRROS: 23.03.2026; Ogledov: 228; Prenosov: 152
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6. Adipose tissue transcriptome profiles of local Krškopolje pig and modern hybrid pigs receving reduced protein diets: : expression profiling by high throughput sequencingKlavdija Poklukar Žnidaršič, Martin Škrlep, Marjeta Čandek-Potokar, 2025, zaključena znanstvena zbirka raziskovalnih podatkov Povzetek: The main objective of this study was to investigate transcriptomic differences in subcutaneous adipose tissue between the local Krškopolje pig and modern hybrids, and to assess the effects of a reduced-protein diet in both genotypes. Comparative analysis between Krškopolje pigs and modern crossbreeds revealed 375 differentially expressed genes, with 189 upregulated and 186 downregulated in Krškopolje pigs. The upregulated genes were enriched in processes related to adipogenesis (SLC7A10, ADIRF, INHBB, SFRP2), extracellular matrix remodeling (COL6A5, COL4A5, COL2A1), calcium signaling (TRPV4, CAMK2A, CALML5), pro-inflammatory cytokines (IL1A, TNFSF9, CXCL8, PTGS2), and cholesterol metabolism (CYP1A1, CYP2A19, CES1). In contrast, the reduced-protein diet induced only minor transcriptional changes at the individual gene level in both Krškopolje pigs and modern crossbreeds.
Ključne besede: RNA sequences, pigs, adipose tissue, high throughput sequencing, RNA, transcriptome profiles, gene expression, locel breeds, hybrid breeds, data, data set
Objavljeno v DiRROS: 20.03.2026; Ogledov: 423; Prenosov: 69
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7. Effect of rearing systems and dietary protein levels on the skeletal muscle histomorphology and transcriptome profiles in indigenous Krškopolje Pig : expression profiling by high throughput sequencingMilka Vrecl, Martin Škrlep, Klavdija Poklukar Žnidaršič, Gregor Fazarinc, Malan Štrbenc, Marjeta Čandek-Potokar, 2026, zaključena znanstvena zbirka raziskovalnih podatkov Povzetek: RNA-sequencing was performed to compare the effects of production systems (conventional indoor, vs. outdoor) and diets (standard protein, HP, vs. low protein, LP) within each rearing system on the transcriptomic profiles of two skeletal muscles, longissimus thoracis et lumborum (LL) and semispinalis capitis (SSC). Differentially expressed genes (DEGs) were identified with |log2FC| > 1 and q-value < 0.005. The effect of rearing system (indoor vs. outdoor) resulted in 354 DEGs in LL and 334 DEGs in SSC. The effect of diet within individual rearing system was less pronounced. In LL, HP vs. LP resulted in 23 DEGs under indoor and none under outdoor rearing system. In SSC, HP vs. LP resulted in 28 DEGs under indoor and 30 DEGs under outdoor rearing system. Pathway enrichment analysis revealed 42 pathways significantly enriched for HP vs. LP in the outdoor rearing system (across both muscles); additionally, 11 pathways were altered specifically in SSC for HP vs. LP under indoor rearing system, and 27 pathways were altered specifically in LL for HP vs. LP under outdoor rearing system
Ključne besede: RNA sequences, pigs, adipose tissue, high throughput sequencing, RNA, transcriptome profiles, gene expression, locel breeds, hybrid breeds, data, data set
Objavljeno v DiRROS: 20.03.2026; Ogledov: 359; Prenosov: 78
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8. On the weak $k$-metric dimension of Hamming graphsElena Fernández, Sandi Klavžar, Dorota Kuziak, Manuel Muñoz-Márquez, Ismael G. Yero, 2026, izvirni znanstveni članek Povzetek: Given a connected graph $G$, a set of vertices $X\subset V(G)$ is a weak $k$-resolving set of $G$ if for each two vertices $y,z\in V(G)$, the sum of the values $|d_G(y,x)-d_G(z,x)|$ over all $x\in X$ is at least $k$, where $d_G(u,v)$ stands for the length of a shortest path between $u$ and $v$. The cardinality of a smallest weak $k$-resolving set of $G$ is the weak $k$-metric dimension of $G$, and is denoted by $\mathrm{wdim}_k(G)$. In this paper, $\mathrm{wdim}_k(K_n\,\square\,K_n)$ is determined for every $n\ge 3$ and every $2\le k\le 2n$. An improvement of a known integer linear programming formulation for this problem is developed and implemented for the graphs $K_n\,\square\,K_m$. Conjectures regarding these general situations are posed.
Ključne besede: weak $k$-metric dimension, weak $k$-resolving set, Cartesian product, Hamming graph
Objavljeno v DiRROS: 13.03.2026; Ogledov: 303; Prenosov: 257
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9. Mutual-visibility problems in Kneser and Johnson graphsGülnaz Boruzanli Ekinci, Csilla Bujtás, 2025, izvirni znanstveni članek Povzetek: Let $G$ be a connected graph and $X \subseteq V(G)$. By definition, two vertices $u$ and $v$ are $X$-visible in $G$ if there exists a shortest $u, v$-path with all internal vertices being outside of the set $X$. The largest size of $X$ such that any two vertices of $G$ (resp. any two vertices from $X$) are $X$-visible is the total mutual-visibility number (resp. the mutual-visibility number) of $G$. In this paper, we determine the total mutual-visibility number of Kneser graphs, bipartite Kneser graphs, and Johnson graphs. The formulas proved for Kneser, and bipartite Kneser graphs are related to the size of transversal-critical uniform hypergraphs, while the total mutual-visibility number of Johnson graphs is equal to a hypergraph Turán number. Exact values or estimates for the mutual-visibility number over these graph classes are also established.
Ključne besede: mutual-visibility set, total mutual-visibility set, Kneser graph, bipartite Kneser graph, Johnson graph, Turán-type problem, covering design
Objavljeno v DiRROS: 05.03.2026; Ogledov: 1675; Prenosov: 211
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10. The $d$-distance $p$-packing domination number: complexity, cycles, and treesCsilla Bujtás, Vesna Iršič Chenoweth, Sandi Klavžar, Gang Zhang, 2026, izvirni znanstveni članek Povzetek: A set of vertices $X\subseteq V(G)$ is a $d$-distance dominating set if for every $u\in V(G)\setminus X$ there exists $x\in X$ such that $d(u,x) \le d$, and $X$ is a $p$-packing if $d(u,v) \ge p+1$ for every different $u,v\in X$. The $d$-distance $p$-packing domination number $\gamma_d^p(G)$ of $G$ is the minimum size of a set of vertices of $G$ which is both a $d$-distance dominating set and a $p$-packing. It is proved that for every two fixed integers $d$ and $p$ with $2 \le d$ and $0 \le p \leq 2d-1$, the decision problem whether $\gamma_d^p(G) \leq k$ holds is NP-complete for bipartite planar graphs. A necessary and sufficient condition for the existence of a $d$-distance $p$-packing dominating set in $C_n$ is obtained and $\gamma_d^p(C_n)$ determined for every $d$, $p$, and $n$. For a tree $T$ on $n$ vertices with $\ell$ leaves and $s$ support vertices it is proved that (i) $\gamma_2^0(T) \geq \frac{n-\ell-s+4}{5}$, (ii) $\left \lceil \frac{n-\ell-s+4}{5} \right \rceil \leq \gamma_2^2(T) \leq \left \lfloor \frac{n+3s-1}{5} \right \rfloor$, and if $d \geq 2$, then (iii) $\gamma_d^2(T) \leq \frac{n-2\sqrt{n}+d+1}{d}$. Inequality (i) improves an earlier bound due to Meierling and Volkmann, and independently Raczek, Lema\'nska, and Cyman, while (iii) extends an earlier result for $\gamma_2^2(T)$ due to Henning. Sharpness of the bounds is discussed and established in most cases. It is also proved that every connected graph $G$ contains a spanning tree $T$ such that $\gamma_2^2(T) \leq \gamma_2^2(G)$.
Ključne besede: d-distance dominating set, p-packing set, dominating set, trees, planar graphs
Objavljeno v DiRROS: 23.02.2026; Ogledov: 350; Prenosov: 275
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