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A lower bound for the circumference of a graph

✍ Scribed by Nathan Linial

Publisher: Elsevier Science
Year: 1976
Tongue: English
Weight: 423 KB
Volume: 15
Category: Article
ISSN: 0012-365X
DOI: 10.1016/0012-365x(76)90031-5

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✦ Synopsis

Lrzt G = (V, 0 be a ttlock :.>f order n, different from Kn. Let ~FI = min {d(x) + d(y): n then G contains a cycle of length at least m. 1. Introductlion and notatio e discuss only finite undirected graphs withsLc loops and multiple edges. We p:rosye the main theorem d show how Qre's th -orem [ 3.1 on Hamiltonian graphs is easily deduc Let 5; = ( V, E) be a graph where ', E are the vertex any! edge #sets respectively. The cardinality of a set ,S is denoted by ISI. II stan out for i VI, the order of @. Y'(x) is the set of vertices adjacent to x. d(x) = ~Rx-)l, the degree ofx A Mrck, or Gquivalently a Z-connected graph is a connected graph whit remitins connected after the deletion Qf any of its vertices. The &x~~#llrence of C, c(G) is the length of the .ngest cycle contained in G. [The I of a path or a cycle is the nu-er of ed 2'9 '7

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