A note on the ultimate categorical matching in a graph

  • Authors:

  • Lih-Hsing Hsu

  • Affiliations:

  • Department of Computer and Information Science, National Chiao Tung University, 1001 Ta Hsueh Road, 300 Hsinchu, Taiwan, ROC

  • Venue:
  • Discrete Mathematics
  • Year:
  • 2002

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Abstract

Let m(G) denote the number of vertices covered by a maximum matching in a graph G. The ultimate categorical matching m*(G) is defined as m*(G) = limn → ∞m(Gn)1/n where the categorical graph product is used. In (Discrete Math. 232 (2001) 1), Albert et al. ask that "Is there a graph G, with at least one edge, such that for all graphs H, m*(G×H) = m*(G)m*(H)?". Actually, m*(G × H)=m*(G)m*(H) holds for any graphs G and H with the previous result of Hsu et al. (Discrete Math, 65 (1987) 53).