Fan-type results for the existence of [ a, b ]-factors

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Abstract

Let 1 ≤ a < b be integers and G a graph of order n sufficiently large for a and b. Then G has an [ a, b ]-factor if the minimum degree is at least a and every pair of vertices distance two apart has cardinality of the neighborhood union at least an / ( a + b ). This lower bound is sharp. As a consequence, we have a Fan-type condition for a graph to have an [ a, b ]-factor.

Original languageEnglish
Pages (from-to)688-693
Number of pages6
JournalDiscrete Mathematics
Volume306
Issue number7
DOIs
Publication statusPublished - 2006 Apr 28
Externally publishedYes

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Keywords

  • [ a, b ]-factor
  • Factor
  • Fan-type
  • Graph
  • Neighborhood union

ASJC Scopus subject areas

  • Discrete Mathematics and Combinatorics
  • Theoretical Computer Science

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