501. The core of a vertex-transitive complementary prismMarko Orel, 2023, izvirni znanstveni članek Povzetek: The complementary prism $\Gamma \overline{\Gamma}$ is obtained from the union of a graph $\Gamma$ and its complement $\overline{\Gamma}$ where each pair of identical vertices in $\Gamma$ and $\overline{\Gamma}$ is joined by an edge. It generalizes the Petersen graph, which is the complementary prism of the pentagon. The core of a vertex-transitive complementary prism is studied. In particular, it is shown that a vertex-transitive complementary prism $\Gamma \overline{\Gamma}$ is a core, i.e. all its endomorphisms are automorphisms, whenever $\Gamma$ is a core or its core is a complete graph.
Ključne besede: graph homomorphism, complementary prism, self-complementary graph, vertex-transitive graph, core
Objavljeno v DiRROS: 09.04.2024; Ogledov: 207; Prenosov: 83
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502. Domination and independence numbers of large 2-crossing-critical graphsVesna Iršič, Maruša Lekše, Miha Pačnik, Petra Podlogar, Martin Praček, 2023, izvirni znanstveni članek Povzetek: After 2-crossing-critical graphs were characterized in 2016, their most general subfamily, large 3-connected 2-crossing-critical graphs, has attracted separate attention. This paper presents sharp upper and lower bounds for their domination and independence number.
Ključne besede: crossing-critical graphs, domination number, independence number
Objavljeno v DiRROS: 09.04.2024; Ogledov: 217; Prenosov: 114
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504. Sliding wear behaviour of conventional and cryotreated PM Cr-V (Vanadis 6) ledeburitic tool steelVenu Yarasu, Peter Jurči, Peter Gogola, Bojan Podgornik, Marko Sedlaček, 2023, izvirni znanstveni članek Ključne besede: cold work tool steel, conventional treatment, cryogenic treatment, hardness, reciprocal sliding, wear
Objavljeno v DiRROS: 08.04.2024; Ogledov: 281; Prenosov: 38
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505. Maximum matchings in geometric intersection graphsÉdouard Bonnet, Sergio Cabello, Wolfgang Mulzer, 2023, izvirni znanstveni članek Povzetek: Let $G$ be an intersection graph of $n$ geometric objects in the plane. We show that a maximum matching in $G$ can be found in $O(\rho^{3\omega/2}n^{\omega/2})$ time with high probability, where $\rho$ is the density of the geometric objects and $\omega>2$ is a constant such that $n \times n$ matrices can be multiplied in $O(n^\omega)$ time. The same result holds for any subgraph of $G$, as long as a geometric representation is at hand. For this, we combine algebraic methods, namely computing the rank of a matrix via Gaussian elimination, with the fact that geometric intersection graphs have small separators. We also show that in many interesting cases, the maximum matching problem in a general geometric intersection graph can be reduced to the case of bounded density. In particular, a maximum matching in the intersection graph of any family of translates of a convex object in the plane can be found in $O(n^{\omega/2})$ time with high probability, and a maximum matching in the intersection graph of a family of planar disks with radii in $[1, \Psi]$ can be found in $O(\Psi^6\log^{11} n + \Psi^{12 \omega} n^{\omega/2})$ time with high probability.
Ključne besede: computational geometry, geometric intersection graphs, disk graphs, unit-disk graphs, matchings
Objavljeno v DiRROS: 08.04.2024; Ogledov: 253; Prenosov: 82
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506. Maker-Breaker domination game on trees when Staller winsCsilla Bujtás, Pakanun Dokyeesun, Sandi Klavžar, 2023, izvirni znanstveni članek 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: 276; Prenosov: 114
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507. The Calabi-Yau problem for minimal surfaces with Cantor endsFranc Forstnerič, 2023, izvirni znanstveni članek Povzetek: We show that every connected compact or bordered Riemann surface contains a Cantor set whose complement admits a complete conformal minimal immersion in ${\mathbb R}^3$ with bounded image. The analogous result holds for holomorphic immersions into any complex manifold of dimension at least $2$, for holomorphic null immersions into ${\mathbb C}^n$ with $n \ge 3$, for holomorphic Legendrian immersions into an arbitrary complex contact manifold, and for superminimal immersions into any selfdual or anti-self-dual Einstein four-manifold.
Ključne besede: minimal surfaces, Calabi–Yau problem, null curve, Legendrian curve
Objavljeno v DiRROS: 08.04.2024; Ogledov: 240; Prenosov: 84
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508. Generalized Pell graphsVesna Iršič, Sandi Klavžar, Elif Tan, 2023, izvirni znanstveni članek Povzetek: In this paper, generalized Pell graphs $\Pi_{n,k}$, $k\ge 2$, are introduced. The special case of $k=2$ are the Pell graphs $\Pi_{n}$ defined earlier by Munarini. Several metric, enumerative, and structural properties of these graphs are established. The generating function of the number of edges of $\Pi_{n,k}$ and the generating function of its cube polynomial are determined. The center of $\Pi_{n,k}$ is explicitly described; if $k$ is even, then it induces the Fibonacci cube $\Gamma_{n}$. It is also shown that $\Pi_{n,k}$ is a median graph, and that $\Pi_{n,k}$ embeds into a Fibonacci cube.
Ključne besede: Fibonacci cubes, Pell graphs, generating functions, center of graph, median graphs, k-Fibonacci sequence
Objavljeno v DiRROS: 08.04.2024; Ogledov: 255; Prenosov: 99
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510. A coupled convective-diffusive model of heat transfer and melt-pool dynamics in additive manufacturingTijan Mede, Matjaž Godec, 2024, elaborat, predštudija, študija Ključne besede: additive manufacturing, selective laser melting, laser powder-bed fusion, melt-pool, heat transfer, convection
Objavljeno v DiRROS: 05.04.2024; Ogledov: 239; Prenosov: 0 |
