Unique intersectability of diamond-free graphs

  • Authors:

  • Jun-Lin Guo;Tao-Ming Wang;Yue-Li Wang

  • Affiliations:

  • Department of Information Management, National Taiwan University of Science and Technology, Taipei, Taiwan, ROC;Department of Mathematics, Tunghai University, Taichung, Taiwan, ROC;Department of Information Management, National Taiwan University of Science and Technology, Taipei, Taiwan, ROC

  • Venue:
  • Discrete Applied Mathematics
  • Year:
  • 2011

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Abstract

For a graph G with vertices v"1,v"2,...,v"n, a simple set representation of G is a family F={S"1,S"2,...,S"n} of distinct nonempty sets such that |S"i@?S"j|=1 if v"iv"j is an edge in G, and |S"i@?S"j|=0 otherwise. Let S(F)=@?"i"="1^nS"i, and let @w"s(G) denote the minimum |S(F)| of a simple set representation F of G. If, for every two minimum simple set representations F and F^' of G, F can be obtained from F^' by a bijective mapping from S(F^') to S(F), then G is said to be s-uniquely intersectable. In this paper, we are concerned with the s-unique intersectability of diamond-free graphs, where a diamond is a K"4 with one edge deleted. Moreover, for a diamond-free graph G, we also derive a formula for computing @w"s(G).