Results 1 to 10 of about 173,561 (110)
Non 1-planarity of lexicographic products of graphs
Discussiones Mathematicae Graph Theory, 2021 zbMATH Open Web Interface contents unavailable due to conflicting licenses.
Matsumoto Naoki, Suzuki Yusuke
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Acyclic Chromatic Index of 1-Planar Graphs
Mathematics, 2022 The acyclic chromatic index χa′(G) of a graph G is the smallest k for which G is a proper edge colorable using k colors. A 1-planar graph is a graph that can be drawn in plane such that every edge is crossed by at most one other edge. In this paper, we prove that every 1-planar graph G has χa′(G)≤Δ+36, where Δ denotes the maximum degree of G.
Wanshun Yang +5 more
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The structure and the list 3-dynamic coloring of outer-1-planar graphs [PDF]
Discrete Mathematics & Theoretical Computer Science, 2021 An outer-1-planar graph is a graph admitting a drawing in the plane so that all vertices appear in the outer region of the drawing and every edge crosses at most one other edge.
Yan Li, Xin Zhang
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Improved product structure for graphs on surfaces [PDF]
Discrete Mathematics & Theoretical Computer Science, 2022 Dujmovi\'c, Joret, Micek, Morin, Ueckerdt and Wood [J. ACM 2020] proved that for every graph $G$ with Euler genus $g$ there is a graph $H$ with treewidth at most 4 and a path $P$ such that $G\subseteq H \boxtimes P \boxtimes K_{\max\{2g,3\}}$. We improve
Marc Distel +3 more
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Correction to: Outer 1-Planar Graphs [PDF]
Algorithmica, 2021 zbMATH Open Web Interface contents unavailable due to conflicting licenses.
Auer, Christopher +6 more
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Packing Trees into 1-planar Graphs [PDF]
Journal of Graph Algorithms and Applications, 2020 We introduce and study the 1-planar packing problem: Given $k$ graphs with $n$ vertices $G_1, \dots, G_k$, find a 1-planar graph that contains the given graphs as edge-disjoint spanning subgraphs. We mainly focus on the case when each $G_i$ is a tree and $k=3$.
Felice De Luca +8 more
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Equitable Coloring of IC-Planar Graphs with Girth g ≥ 7
Axioms, 2023 An equitable k-coloring of a graph G is a proper vertex coloring such that the size of any two color classes differ at most 1. If there is an equitable k-coloring of G, then the graph G is said to be equitably k-colorable.
Danjun Huang, Xianxi Wu
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From light edges to strong edge-colouring of 1-planar graphs [PDF]
Discrete Mathematics & Theoretical Computer Science, 2020 A strong edge-colouring of an undirected graph $G$ is an edge-colouring where every two edges at distance at most~$2$ receive distinct colours. The strong chromatic index of $G$ is the least number of colours in a strong edge-colouring of $G$.
Julien Bensmail +3 more
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Discussiones Mathematicae Graph Theory, 2023 DP-coloring is generalized via relaxed coloring and variable degeneracy in [P. Sittitrai and K. Nakprasit, Su cient conditions on planar graphs to have a relaxed DP-3-coloring, Graphs Combin. 35 (2019) 837–845], [K.M. Nakprasit and K.
Sribunhung Sarawute +3 more
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Counting cliques in 1-planar graphs
European Journal of Combinatorics, 2023 The problem of maximising the number of cliques among n-vertex graphs from various graph classes has received considerable attention. We investigate this problem for the class of 1-planar graphs where we determine precisely the maximum total number of cliques as well as the maximum number of cliques of any fixed size. We also precisely characterise the
Gollin, J. Pascal +4 more
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