Restricted b-matchings in degree-bounded graphs

  • Authors:
  • Kristóf Bérczi;László A. Végh

  • Affiliations:
  • MTA-ELTE Egerváry Research Group (EGRES), Department of Operations Research, Eötvös Loránd University, Budapest, Hungary;MTA-ELTE Egerváry Research Group (EGRES), Department of Operations Research, Eötvös Loránd University, Budapest, Hungary

  • Venue:
  • IPCO'10 Proceedings of the 14th international conference on Integer Programming and Combinatorial Optimization
  • Year:
  • 2010

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Abstract

We present a min-max formula and a polynomial time algorithm for a slight generalization of the following problem: in a simple undirected graph in which the degree of each node is at most t+1, find a maximum t-matching containing no member of a list $\mathcal{K}$ of forbidden Kt,t and Kt+1 subgraphs. An analogous problem for bipartite graphs without degree bounds was solved by Makai [15], while the special case of finding a maximum square-free 2-matching in a subcubic graph was solved in [1].