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Autor:
Zhang, Licheng, Huang, Yuanqiu
A graph is reducible if it is the lexicographic product of two smaller non-trivial graphs. It is well-known a 1-planar graph with $n ~(\ge3)$ vertices has at most $4n-8$ edges, and a graph $G$ with $n$ vertices is optimal if $G$ has exactly $4n-8$ ed
Externí odkaz:
http://arxiv.org/abs/2211.14733
Path-addition is an operation that takes a graph and adds an internally vertex-disjoint path between two vertices together with a set of supplementary edges. Path-additions are just the opposite of taking minors. We show that some classes of graphs a
Externí odkaz:
http://arxiv.org/abs/1605.02891
Autor:
Zhang, Licheng, Huang, Yuanqiu
A graph is called 1-planar if it can be drawn on the plane (or on the sphere) such that each edge is crossed at most once. A 1-planar graph $G$ is called optimal if it satisfies $|E(G)| = 4|V(G)|-8$. If $G$ and $H$ are graphs, then the lexicographic
Externí odkaz:
https://explore.openaire.eu/search/publication?articleId=doi_dedup___::a4084f0194f4f38fc0bc83577f28f54b
http://arxiv.org/abs/2211.14733
http://arxiv.org/abs/2211.14733