Results 11 to 20 of about 51 (50)
The crossing number of the generalized Petersen graph P(3k,k) in the projective plane
AKCE International Journal of Graphs and Combinatorics, 2023 The crossing number of a graph G in a surface Σ, denoted by [Formula: see text], is the minimum number of pairwise intersections of edges in a drawing of G in Σ. Let k be an integer satisfying [Formula: see text], the generalized Petersen graph [Formula:
Jing Wang, Zuozheng Zhang
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On characterizing proper max-point-tolerance graphs
AKCE International Journal of Graphs and Combinatorics, 2023 Max-point-tolerance graphs (MPTG) were introduced by Catanzaro et al. in 2017 as a generalization of interval graphs. This graph class has many practical applications in the study of the human genome as well as in signal processing for networks. The same
Sanchita Paul
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Annular and pants thrackles [PDF]
Discrete Mathematics & Theoretical Computer Science, 2018 A thrackle is a drawing of a graph in which each pair of edges meets precisely once. Conway's Thrackle Conjecture asserts that a thrackle drawing of a graph on the plane cannot have more edges than vertices.
Grace Misereh, Yuri Nikolayevsky
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Old and new generalizations of line graphs
International Journal of Mathematics and Mathematical Sciences, Volume 2004, Issue 29, Page 1509-1521, 2004., 2004 Line graphs have been studied for over seventy years. In 1932, H. Whitney showed that for connected graphs, edge‐isomorphism implies isomorphism except for K3 and K1,3. The line graph transformation is one of the most widely studied of all graph transformations.
Jay Bagga
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Homomorphic Preimages of Geometric Paths
Discussiones Mathematicae Graph Theory, 2018 A graph G is a homomorphic preimage of another graph H, or equivalently G is H-colorable, if there exists a graph homomorphism f : G → H. A geometric graph Ḡ is a simple graph G together with a straight line drawing of G in the plane with the vertices in
Cockburn Sally
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A Note on the Crossing Numbers of 5-Regular Graphs
Discussiones Mathematicae Graph Theory, 2020 The crossing number cr(G) of a graph G is the smallest number of edge crossings in any drawing of G. In this paper, we prove that there exists a unique 5-regular graph G on 10 vertices with cr(G) = 2.
Ouyang Zhangdong
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Requiring that Minimal Separators Induce Complete Multipartite Subgraphs
Discussiones Mathematicae Graph Theory, 2018 Complete multipartite graphs range from complete graphs (with every partite set a singleton) to edgeless graphs (with a unique partite set). Requiring minimal separators to all induce one or the other of these extremes characterizes, respectively, the ...
McKee Terry A.
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On An Extremal Problem In The Class Of Bipartite 1-Planar Graphs
Discussiones Mathematicae Graph Theory, 2016 A graph G = (V, E) is called 1-planar if it admits a drawing in the plane such that each edge is crossed at most once. In this paper, we study bipartite 1-planar graphs with prescribed numbers of vertices in partite sets.
Czap Július +2 more
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The Crossing Number of The Hexagonal Graph H3,n
Discussiones Mathematicae Graph Theory, 2019 In [C. Thomassen, Tilings of the torus and the Klein bottle and vertex-transitive graphs on a fixed surface, Trans. Amer. Math. Soc. 323 (1991) 605–635], Thomassen described completely all (except finitely many) regular tilings of the torus S1 and the ...
Wang Jing +2 more
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Sharp Upper Bounds on the Clar Number of Fullerene Graphs
Discussiones Mathematicae Graph Theory, 2018 The Clar number of a fullerene graph with n vertices is bounded above by ⌊n/6⌋ − 2 and this bound has been improved to ⌊n/6⌋ − 3 when n is congruent to 2 modulo 6.
Gao Yang, Zhang Heping
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