Domination numbers and homology

  • Authors:

  • Roy Meshulam

  • Affiliations:

  • Department of Mathematics, Technion, Haifa 32000, Israel

  • Venue:
  • Journal of Combinatorial Theory Series A
  • Year:
  • 2003

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Abstract

Let I(G) denote the independence complex of a graph G = (V, E). Some relations between domination numbers of G and the homology of I(G) are given. As a consequence the following Hall-type conjecture of Aharoni is proved: Let γs*(G) denote the fractional star-domination number of G and let V =∪i=1m Vi be a partition of V into m classes.If γs*(G[∪i∈I Vi]) |I| - 1 for all I ⊂ {1,...,m} then G contains an independent set which intersects all m classes.