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• W2189902912 abstract "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 girth. We proved that: If G is a graph with δ(G)=2, average degree less than 145 and without (2,2,∞)-triangles, then G has one of the following configurations: a (2,2,13−,2)-path, a (2,3−,3−)-path and a (4;2,2,2,3−)-star. If G is a plane graph with δ(G)≥2 and face size at least 7, then G has a (2,2,5−)-path, or a (2,5−,2)-path or a (3,3,2,3)-path. If G is a graph with δ(G)=2, average degree less than 3 and without (2,2,∞)-triangles, then G has one of the following configurations: a (2,3−,3−)-path, a (2,2,∞,2)-path, a (2,2,4,3)-path, a (4;2,2,2,6−)-star, a (4;2,2,3,5−)-star, a (4;2,3,3,3)-star, a (5;2,2,2,2,2)-star and a (5;2,2,2,2,3)-star. If G is a graph with δ(G)=2, average degree less than 3 and without (2,2,∞)-triangles, then G has one of the following configurations: a (2,3−,3−)-path, a (2,2,∞,2)-path, a (2,2,4,3)-path, a (4;2,2,2,6−)-star, a (2,4,3,2)-path, a (2,4,3)-triangle, a (5;2,2,2,2,2)-star and a (5;2,2,2,2,3)-star. If G is a graph with δ(G)≥2 and average degree less than 103, then G has one of the following configurations: a (2,2,∞)-path, a (2,3,6−)-path, a (3,3,3)-path, a (2,4,3−)-path and a (2,9−,2)-path. If G is a graph with δ(G)=3 and average degree less than 4, then G contains a (4−,3,7−)-path, or a (5,3,5)-path or a (5,3,6)-path. If G is a triangle-free normal plane map, then it contains one of the following configurations: a (3,3,3)-path, a (3,3,4)-path, a (3,3,5,3)-path, a (4,3,4)-path, a (4,3,5)-path, a (5,3,5)-path, a (5,3,6)-path and a (3,4,3)-path." @default.
• W2189902912 created "2016-06-24" @default.
• W2189902912 creator A5040101942 @default.
• W2189902912 date "2016-10-01" @default.
• W2189902912 modified "2023-09-29" @default.
• W2189902912 title "Light subgraphs in graphs with average degree at most four" @default.
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• W2189902912 doi "https://doi.org/10.1016/j.disc.2016.04.020" @default.
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