Light subgraphs in graphs with average degree at most four

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Light subgraphs in graphs with average degree at most four

A graph H is said to be light in a family G of graphs if at least one member of G contains a copy of H and there exists an integer λ(H,G) such that each member G of G with a copy of H also has a copy K of H such that degG(v) ≤ λ(H,G) for all v ∈ V(K). In this paper, we study the light graphs in the class of graphs with small average degree, including the plane graphs with some restrictions on g...

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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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ژورنال

عنوان ژورنال: Discrete Mathematics

سال: 2016

ISSN: 0012-365X

DOI: 10.1016/j.disc.2016.04.020