Light edges in degree-constrained graphs
نویسندگان
چکیده
Let denote the average degree, and Æ denote the minimum degree of a graph. An edge is light if both its endpoints have degree bounded by a constant depending only on and Æ. A graph is degree-constrained if < 2Æ. The primary result of this paper is that every degree-constrained graph has a light edge. Most previous results in this direction have been for embedded graphs. This result is extended in a variety of ways. First it is proved that there exists a constant ( ; Æ) such that for every 0 < ( ; Æ), every degree-constrained graph with n vertices has at least n light edges. An analogous result is proved guaranteeing a matching of light edges. The method is refined in the case of planar graphs to obtain improved degree bounds. keywords: graph, light edge, matching.
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