Light subgraphs of order at most 3 in large maps of minimum degree 5 on compact 2-manifolds
نویسندگان
چکیده
منابع مشابه
Light subgraphs of order 4 in large maps of minimum degree 5 on compact 2-manifolds
A graph H is said to be light in a class G of graphs if at least one member of G contains a copy of H and there is an integer w(H,G) such that each member G of G with a subgraph isomorphic with H has also a copy H with degree sum ∑ x∈V (H) degG(x) ≤ w(H,G). In this paper we prove that all proper spanning subgraphs H of the complete graph K4 are light in the class G of large graphs of minimum de...
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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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A subgraph of a plane graph is light if the sum of the degrees of the vertices of the subgraph in the graph is small. It is well known that a plane graph of minimum degree five contains light edges and light triangles. In this paper we show that every plane graph of minimum degree five contains also light stars K1,3 and K1,4 and a light 4-path P4. The results obtained for K1,3 and P4 are best p...
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Let k be an integer and M be a closed 2-manifold with Euler characteristic χ(M) ≤ 0. We prove that each polyhedral map G on M with minimum degree δ and large number of vertices contains a k-path P , a path on k vertices, such that: (i) for δ ≥ 4 every vertex of P has, in G, degree bounded from above by 6k − 12, k ≥ 8 (It is also shown that this bound is tight for k even and that for k odd this ...
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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: European Journal of Combinatorics
سال: 2005
ISSN: 0195-6698
DOI: 10.1016/j.ejc.2004.01.013