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The minimum number of edges in graphs with prescribed paths

✍ Scribed by Nicholas Pippenger


Publisher
Springer
Year
1978
Tongue
English
Weight
919 KB
Volume
12
Category
Article
ISSN
1433-0490

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Let H=(V H , E H ) be a graph, and let k be a positive integer. A graph G=(V G , E G ) is H-coverable with overlap k if there is a covering of the edges of G by copies of H such that no edge of G is covered more than k times. Denote by overlap(H, G) the minimum k for which G is H-coverable with over

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A simple graph with n vertices is called Pi-connected if any two distinct vertices are connected by an elementary path of length i. In this paper, lower bounds of the number of edges in graphs that are both Pz-and Pi-connected are obtained. Namely if i ~j(n + I), then JE(G)I 3((4i -5)1(2i -2))(n -11