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Povzetek: In the Maker-Breaker domination game played on a graph $G$, Dominator's goal is to select a dominating set and Staller's goal is to claim a closed neighborhood of some vertex. We study the cases when Staller can win the game. If Dominator (resp., Staller) starts the game, then $\gamma_{\rm SMB}(G)$ (resp., $\gamma_{\rm SMB}'(G)$) denotes the minimum number of moves Staller needs to win. For every positive integer $k$, trees $T$ with $\gamma_{\rm SMB}'(T)=k$ are characterized and a general upper bound on $\gamma_{\rm SMB}'$ is proved. Let $S = S(n_1,\dots, n_\ell)$ be the subdivided star obtained from the star with $\ell$ edges by subdividing its edges $n_1-1, \ldots, n_\ell-1$ times, respectively. Then $\gamma_{\rm SMB}'(S)$ is determined in all the cases except when $\ell\ge 4$ and each $n_i$ is even. The simplest formula is obtained when there are at least two odd $n_i$s. If ▫$n_1$▫ and $n_2$ are the two smallest such numbers, then $\gamma_{\rm SMB}'(S(n_1,\dots, n_\ell))=\lceil \log_2(n_1+n_2+1)\rceil$▫. For caterpillars, exact formulas for $\gamma_{\rm SMB}$ and for $\gamma_{\rm SMB}'$ are established.
Ključne besede: domination game, Maker-Breaker game, Maker-Breaker domination game, hypergraphs, trees, subdivided stars, caterpillars
Objavljeno v DiRROS: 08.04.2024; Ogledov: 76; Prenosov: 37
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Povzetek: A subset of vertices of a graph $G$ is a general position set if no triple of vertices from the set lie on a common shortest path in $G$. In this paper we introduce the general position polynomial as $\sum_{i \geq 0} a_i x^i$, where $a_i$ is the number of distinct general position sets of $G$ with cardinality $i$. The polynomial is considered for several well-known classes of graphs and graph operations. It is shown that the polynomial is not unimodal in general, not even on trees. On the other hand, several classes of graphs, including Kneser graphs $K(n,2)$, with unimodal general position polynomials are presented.
Ključne besede: general position set, general position number, general position polynomial, unimodality, trees, Cartesian product of graphs, Kneser graphs
Objavljeno v DiRROS: 28.02.2024; Ogledov: 98; Prenosov: 74
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Povzetek: New mutations provide the raw material for evolution and adaptation. The distribution of fitness effects (DFE) describes the spectrum of effects of new mutations that can occur along a genome, and is, therefore, of vital interest in evolutionary biology. Recent work has uncovered striking similarities in the DFE between closely related species, prompting us to ask whether there is variation in the DFE among populations of the same species, or among species with different degrees of divergence, that is whether there is variation in the DFE at different levels of evolution. Using exome capture data from six tree species sampled across Europe we characterized the DFE for multiple species, and for each species, multiple populations, and investigated the factors potentially influencing the DFE, such as demography, population divergence, and genetic background. We find statistical support for the presence of variation in the DFE at the species level, even among relatively closely related species. However, we find very little difference at the population level, suggesting that differences in the DFE are primarily driven by deep features of species biology, and those evolutionarily recent events, such as demographic changes and local adaptation, have little impact.
Ključne besede: DFE, deleterious mutations, population structure, forest trees
Objavljeno v DiRROS: 12.12.2023; Ogledov: 220; Prenosov: 94
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Povzetek: Cessation of xylem formation or wood growth (CWG) and onset of foliar senescence (OFS) are key autumn phenological events in temperate deciduous trees. Their timing is fundamental for development and survival of trees, ecosystem nutrient cycling, the seasonal exchange of matter and energy between the biosphere and atmosphere and affect the impact and feedback of forests to global change. A large-scale experimental effort and improved observational methods have allowed us to compare the timing of CWG and OFS for different deciduous tree species in Western Europe, in particularly silver birch, a pioneer species, and European beech, a late-succession species, at stands of different latitudes, of different levels of site fertility, and for two years with contrasting meteorological and drought conditions i.e., the low-moderately dry 2017 and the extremely dry 2018. Specifically, we tested whether foliar senescence started before, after or concurrently with CWG. OFS and CWG occurred generally between late September and early November, with larger differences across species and sites for OFS. Foliar senescence started concurrently with CWG in most cases, except for the drier 2018 and, for beech, at the coldest site, where OFS occurred significantly later than CWG. Behavior of beech in Spain, the southern edge of its European distribution, was unclear, with no CWG, but very low wood growth at the time of OFS. Our study suggests that OFS is generally triggered by the same drivers of CWG or when wood growth decreases in late summer, indicating an overarching mechanism of sink limitation as a possible regulator of the timing of foliar senescence.
Ključne besede: autumn phenology, xylem formation, foliar senescence, cambium, chlorophyll, radial growth, wood, decidiuous trees, common aspen, common beech, pedunculate oak, silver birch
Objavljeno v DiRROS: 10.06.2020; Ogledov: 1899; Prenosov: 1138
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