Results 11 to 20 of about 28,812 (264)
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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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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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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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
Jochen Pascal Gollin +4 more
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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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On Drawings and Decompositions of 1-Planar Graphs [PDF]
The Electronic Journal of Combinatorics, 2013 A graph is called 1-planar if it can be drawn in the plane so that each of its edges is crossed by at most one other edge. We show that every 1-planar drawing of any 1-planar graph on $n$ vertices has at most $n-2$ crossings; moreover, this bound is tight.
Július Czap, Dávid Hudák
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Drawing Subcubic 1-Planar Graphs with Few Bends, Few Slopes, and Large Angles
Journal of Graph Algorithms and Applications, 2021 We show that the $1$-planar slope number of $3$-connected cubic $1$-planar graphs is at most four when edges are drawn as polygonal curves with at most one bend each, that is, any such graph admits a drawing with at most one bend per edge and such that ...
Philipp Kindermann +3 more
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Cops and Robbers on 1-Planar Graphs
, 2023 Cops and Robbers is a well-studied pursuit-evasion game in which a set of cops seeks to catch a robber in a graph G, where cops and robber move along edges of G. The cop number of G is the minimum number of cops that is sufficient to catch the robber. Every planar graph has cop number at most three, and there are planar graphs for which three cops are ...
Stephane Durocher +8 more
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Computational Study on a PTAS for Planar Dominating Set Problem
Algorithms, 2013 The dominating set problem is a core NP-hard problem in combinatorial optimization and graph theory, and has many important applications. Baker [JACM 41,1994] introduces a k-outer planar graph decomposition-based framework for designing polynomial time ...
Qian-Ping Gu, Marjan Marzban
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On (p, 1)-Total Labelling of Some 1-Planar Graphs
Discussiones Mathematicae Graph Theory, 2021 A graph is 1-planar if it can be drawn on the plane so that each edge is crossed by at most one other edge. In this paper, it is proved that the (p, 1)-total labelling number (p ≥ 2) of every 1-planar graph G is at most Δ(G) + 2p − 2 provided that Δ (G) ≥
Niu Bei, Zhang Xin
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