Results 21 to 30 of about 27,017 (285)
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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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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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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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.
Czap, Július, Hudák, Dávid
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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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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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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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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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Acyclic colouring of 1-planar graphs
Discrete Applied Mathematics, 2001 A graph is said to be 1-planar if it can be embedded into the plane so that each of its edges is crossed by at most one other edge. A coloring of the vertices of a graph is said to be acyclic if every cycle contains at least three colors. The acyclic chromatic number \(a(G)\) of a graph \(G\) is the minimal \(k\) such that \(G\) admits an acyclic \(k\)-
Borodin, O. V. +3 more
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