Results 1 to 10 of about 143,935 (124)
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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Mathematical Modelling and Control, 2021 In this paper, we study the problem of partitioning the vertex set of a planar graph with girth restriction into parts, also referred to as color classes, such that each part induces a graph with components of bounded order.
Chunyu Tian, Lei Sun
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On the planarity of line Mycielskian graph of a graph
Ratio Mathematica, 2020 The line Mycielskian graph of a graph G, denoted by Lμ(G) is defined as the graph obtained from L(G) by adding q+1 new vertices E' = ei' : 1 ≤ i ≤ q and e, then for 1 ≤ i ≤ q , joining ei' to the neighbours of ei and to e.
Keerthi G. Mirajkar +1 more
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The k-subconnectedness of planar graphs
AIMS Mathematics, 2021 A graph G with at least 2k vertices is called k-subconnected if, for any 2k vertices x1,x2,⋯,x2k in G, there are k independent paths joining the 2k vertices in pairs in G.
Zongrong Qin, Dingjun Lou
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Links in projective planar graphs [PDF]
Involve 18 (2025) 199-238, 2022 A graph $G$ is nonseparating projective planar if $G$ has a projective planar embedding without a nonsplit link. Nonseparating projective planar graphs are closed under taking minors and are a superclass of projective outerplanar graphs. We partially characterize the minor-minimal separating projective planar graphs by proving that given a minor ...
arxiv +1 more source
A bipartite graph associated to elements and cosets of subgroups of a finite group
AIMS Mathematics, 2021 Let $ G $ be a finite group. A bipartite graph associated to elements and cosets of subgroups of $ G $ is the simple undirected graph $ \Gamma(G) $ with the vertex set $ V(\Gamma(G)) = A\cup B $, where $ A $ is the set of all elements of a group $ G ...
Saba Al-Kaseasbeh, Ahmad Erfanian
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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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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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A note on nearly Platonic graphs with connectivity one
Electronic Journal of Graph Theory and Applications, 2021 A k-regular planar graph G is nearly Platonic when all faces but one are of the same degree while the remaining face is of a different degree. We show that no such graphs with connectivity one can exist. This complements a recent result by Keith, Froncek,
Dalibor Froncek +3 more
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