Results 21 to 30 of about 200,785 (277)
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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Joins of 1-planar graphs [PDF]
Acta Mathematica Sinica, English Series, 2014 A graph is called 1-planar if there exists its drawing in the plane such that each edge is crossed at most once. In this paper, we study 1-planar graph joins. We prove that the join $G+H$ is 1-planar if and only if the pair $[G,H]$ is subgraph-majorized (that is, both $G$ and $H$ are subgraphs of graphs of the major pair) by one of pairs $[C_3 \cup C_3,
Czap, J��lius +2 more
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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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Right Angle Crossing Graphs and 1-Planarity [PDF]
Discrete Applied Mathematics, 2012 zbMATH Open Web Interface contents unavailable due to conflicting licenses.
Eades Peter, LIOTTA, Giuseppe
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The small intersection graph of filters of a bounded distributive lattice [PDF]
Journal of Mahani Mathematical Research, 2023 Let $L$ be a lattice with $1$ and $0$. The small intersection graph of filters of $L$, denoted by $\Gamma(L)$, is defined to be a graph whose vertices are in one to one correspondence with all non-trivial filters of $L$ and two distinct vertices are ...
Shahabaddin Ebrahimi Atani +2 more
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Linear Arboricity of Outer-1-Planar Graphs [PDF]
Journal of the Operations Research Society of China, 2019 zbMATH Open Web Interface contents unavailable due to conflicting licenses.
Xin Zhang, Bi Li
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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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The Stub Resolution of 1-Planar Graphs
Journal of Graph Algorithms and Applications, 2020 The resolution of a drawing plays a crucial role when defining criteria for its quality. In the past, grid resolution, edge-length resolution, angular resolution and crossing resolution have been investigated. In this paper, we investigate the stub resolution, a recently introduced criterion for nonplanar drawings. Intersection points divide edges into
Kaufmann, Michael +5 more
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On edge colorings of 1-planar graphs [PDF]
Information Processing Letters, 2011 zbMATH Open Web Interface contents unavailable due to conflicting licenses.
Zhang, Xin, Wu, Jian-Liang
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About Structure of Graph Obstructions for Klein Surface with 9 Vertices
Кібернетика та комп'ютерні технології, 2020 The structure of the 9 vertex obstructive graphs for the nonorientable surface of the genus 2 is established by the method of (-transformations of the graphs.
V.I. Petrenjuk, D.A. Petrenjuk
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