Results 1 to 10 of about 282,676 (357)
The number of planar graphs and properties of random planar graphs [PDF]
Discrete Mathematics & Theoretical Computer Science, 2005 We show an asymptotic estimate for the number of labelled planar graphs on $n$ vertices. We also find limit laws for the number of edges, the number of connected components, and other parameters in random planar graphs.
Omer Gimenez, Marc Noy
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Bifurcation, chaotic behaviors and solitary wave solutions for the fractional Twin-Core couplers with Kerr law non-linearity [PDF]
Scientific ReportsThe main purpose of this article is to analyze the bifurcation, chaotic behaviors, and solitary wave solutions of the fractional Twin-Core couplers with Kerr law non-linearity by using the planar dynamical system method.
Zhao Li, Jingjing Lyu, Ejaz Hussain
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Total Coloring of Dumbbell Maximal Planar Graphs
Mathematics, 2022 The Total Coloring Conjecture (TCC) states that every simple graph G is totally (Δ+2)-colorable, where Δ denotes the maximum degree of G. In this paper, we prove that TCC holds for dumbbell maximal planar graphs.
Yangyang Zhou +3 more
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On the expected number of perfect matchings in cubic planar graphs [PDF]
, 2021 A well-known conjecture by Lov\'asz and Plummer from the 1970s asserted that a bridgeless cubic graph has exponentially many perfect matchings. It was solved in the affirmative by Esperet et al. (Adv. Math. 2011).
Noy, Marc +2 more
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AKCE International Journal of Graphs and Combinatorics, 2023 The smallest integer k needed for the assignment of k colors to the elements so that the coloring is proper (vertices and edges) is called the total chromatic number of a graph.
Jayabalan Geetha +2 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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Links in projective planar graphs [PDF]
Involve 18 (2025) 199-238, 2022 A graph $G$ is nonseparating projective planar if $G$ has a projective planar embedding without a nonsplit link. Nonseparating projective planar graphs are closed under taking minors and are a superclass of projective outerplanar graphs. We partially characterize the minor-minimal separating projective planar graphs by proving that given a minor ...
arxiv +1 more source
Total Coloring of Claw-Free Planar Graphs
Discussiones Mathematicae Graph Theory, 2022 A total coloring of a graph is an assignment of colors to both its vertices and edges so that adjacent or incident elements acquire distinct colors. Let Δ(G) be the maximum degree of G.
Liang Zuosong
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Star edge coloring of $ K_{2, t} $-free planar graphs
AIMS Mathematics, 2023 The star chromatic index of a graph $ G $, denoted by $ \chi{'}_{st}(G) $, is the smallest number of colors required to properly color $ E(G) $ such that every connected bicolored subgraph is a path with no more than three edges.
Yunfeng Tang , Huixin Yin , Miaomiao Han
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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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