Results 21 to 30 of about 30,213,529 (145)
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
openaire +6 more sources
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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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.
Wanshun Yang +5 more
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Parameterized Complexity of 1-Planarity
Journal of Graph Algorithms and Applications, 2018 We consider the problem of drawing graphs with at most one crossing per edge. These drawings, and the graphs that can be drawn in this way, are called $1$-planar.
Michael Bannister +2 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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Minimum Cycle Base of Graphs Identified by Two Planar Graphs [PDF]
, 2007 In this paper, we study the minimum cycle base of the planar graphs obtained from two 2-connected planar graphs by identifying an edge (or a cycle) of one graph with the corresponding edge (or cycle) of another, related with map geometries, i.e ...
Han, Ren, Dengju, Ma
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Bar 1-Visibility Graphs and their relation to other Nearly Planar Graphs
Journal of Graph Algorithms and Applications, 2014 A graph is called a strong (resp. weak) bar 1-visibility graph if its vertices can be represented as horizontal segments (bars) in the plane so that its edges are all (resp.
William Evans +4 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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A First Order Logic Definition of Beyond-Planar Graphs
Journal of Graph Algorithms and Applications, 2018 Beyond-planarity is a collective term for classes of graphs that extend the planar graphs and are defined by drawings with restrictions on crossings. Examples are 1-planar, fan-planar, fan-crossing free, and quasi-planar graphs. We define these and other
Franz Brandenburg
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On Weak Flexibility in Planar Graphs [PDF]
, 2020 Recently, Dvo\v{r}\'ak, Norin, and Postle introduced flexibility as an extension of list coloring on graphs [JGT 19']. In this new setting, each vertex $v$ in some subset of $V(G)$ has a request for a certain color $r(v)$ in its list of colors $L(v ...
Murphy, Kyle +3 more
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