Light edges in 1-planar graphs of minimum degree 3
نویسندگان
چکیده
منابع مشابه
Light edges in 1-planar graphs with prescribed minimum degree
A graph is called 1-planar if it can be drawn in the plane so that each edge is crossed by at most one other edge. We prove that each 1-planar graph of minimum degree δ ≥ 4 contains an edge with degrees of its endvertices of type (4,≤ 13) or (5,≤ 9) or (6,≤ 8) or (7, 7). We also show that for δ ≥ 5 these bounds are best possible and that the list of edges is minimal (in the sense that, for each...
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Let G be the class of simple planar graphs of minimum degree ≥ 4 in which no two vertices of degree 4 are adjacent. A graph H is light in G if there is a constant w such that every graph in G which has a subgraph isomorphic to H also has a subgraph isomorphic to H whose sum of degrees in G is ≤ w. Then we also write w(H) ≤ w. It is proved that the cycle Cs is light if and only if 3 ≤ s ≤ 6, whe...
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The old well-known result of Chartrand, Kaugars and Lick [1] says that every k-connected graph G with minimum degree at least 3k/2 has a vertex v such that G− v is still k-connected. In this paper, we consider a generalization of the above result. We prove the following result: Suppose G is a k-connected graph with minimum degree at least 3k/2 + 2. Then G has an edge e such that G− V (e) is sti...
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ژورنال
عنوان ژورنال: Discrete Mathematics
سال: 2020
ISSN: 0012-365X
DOI: 10.1016/j.disc.2019.111664