Regular subgraphs of almost regular graphs

N. Alon, S. Friedland, G. Kalai

Research output: Contribution to journalArticle

57 Scopus citations

Abstract

Suppose every vertex of a graph G has degree k or k + 1 and at least one vertex has degree k + 1. It is shown that if k ≥ 2q - 2 and q is a prime power then G contains a q-regular subgraph (and hence an r-regular subgraph for all r < q, r ≡ q (mod 2)). It is also proved that every simple graph with maximal degree Δ ≥ 2q - 2 and average degree d > ( (2q - 2) (2q - 1))(Δ + 1), where q is a prime power, contains a q-regular subgraph (and hence an r-regular subgraph for all r < q, r ≡ q (mod 2)). These results follow from Chevalley's and Olson's theorems on congruences.

Original languageEnglish (US)
Pages (from-to)79-91
Number of pages13
JournalJournal of Combinatorial Theory, Series B
Volume37
Issue number1
DOIs
StatePublished - Aug 1984
Externally publishedYes

All Science Journal Classification (ASJC) codes

  • Theoretical Computer Science
  • Discrete Mathematics and Combinatorics
  • Computational Theory and Mathematics

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