Results 31 to 40 of about 547,177 (325)
On local properties of 1-planar graphs with high minimum degree
Ars Math. Contemp., 2011 A graph is called 1-planar if there exists its drawing in the plane such that each edge contains at most one crossing. We prove that each 1-planar graph of minimum degree 7 contains a pair of adjacent vertices of degree 7 as well as several small graphs ...
David E. Hudak, Tomáš Madaras
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On the lightness of chordal 4-cycle in 1-planar graphs with high minimum degree
Ars Math. Contemp., 2013 A graph G is 1 -planar if it can be drawn on the plane so that each edge is crossed by at most one other edge. The family of 1-planar graphs with minimum vertex degree at least δ and minimum edge degree at least ɛ is denoted by P δ 1 ( ɛ ) .
Xin Zhang, Guizhen Liu
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On properties of maximal 1-planar graphs
Discussiones Mathematicae Graph Theory, 2012 Department of Mathematics, Faculty of ScienceNiigata University8050, Ikarashi 2-no-cho, Nishi-ku, Niigata, 950-2181, Japane-mail: y-suzuki@math.sc.niigata-u.ac.jpAbstractA graph is called 1-planar if there exists a drawing in the plane so thateach edge ...
Dávid Hudák, T. Madaras, Yusuke Suzuki
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On the Book Thickness of 1-Planar Graphs [PDF]
arXiv, 2015 In a book embedding of a graph G, the vertices of G are placed in order along a straight-line called spine of the book, and the edges of G are drawn on a set of half-planes, called the pages of the book, such that two edges drawn on a page do not cross each other. The minimum number of pages in which a graph can be embedded is called the book-thickness
Alam, Md. Jawaherul +2 more
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Acyclic edge coloring of triangle-free 1-planar graphs [PDF]
, 2015 Wen Yao Song, Lian Ying Miao
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On the Size of Matchings in 1-Planar Graph with High Minimum Degree [PDF]
SIAM Journal on Discrete Mathematics, 2022 A matching of a graph is a set of edges without common end vertex. A graph is called 1-planar if it admits a drawing in the plane such that each edge is crossed at most once.
Yuanqiu Huang, Zhangdong Ouyang, F. Dong
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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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Right Angle Crossing Graphs and 1-Planarity [PDF]
Discrete Applied Mathematics, 2011 A Right Angle Crossing Graph (also called RAC graph for short) is a graph that has a straight-line drawing where any two crossing edges are orthogonal to each other. A 1-planar graph is a graph that has a drawing where every edge is crossed at most once.
Peter Eades, Giuseppe Liotta
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On the Sizes of Bipartite 1-Planar Graphs [PDF]
The Electronic Journal of Combinatorics, 2021 A graph is called $1$-planar if it admits a drawing in the plane such that each edge is crossed at most once. Let $G$ be a bipartite $1$-planar graph with $n$ ($n\ge 4$) vertices and $m$ edges. Karpov showed that $m\le 3n-8$ holds for even $n\ge 8$ and $m\le 3n-9$ holds for odd $n\ge 7$.
Dong, F. M. +2 more
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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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