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Paper   IPM / M / 102
School of Mathematics
  Title:   Characterization of graphs with Hall index 2
1.  Ch. Eslahchi
2.  M.L. Mehrabadi
  Status:   Published
  Journal: Australas. J. Combin.
  Vol.:  21
  Year:  2000
  Pages:   13-21
  Supported by:  IPM
A proper edge coloring of a simple graph G from some lists assigned to the edges of G is of interest. A. Hilton and P. Johnson (1990) considered a necessary condition for the list coloring of a graph and called it Hall's condition. They introduced the Hall index of a graph G, h′(G), as the smallest positive integer m such that there exists a list coloring whenever the lists are of length at least m and Hall's condition is satisfied. They characterized all graphs G with h′(G)=1. In this paper we characterize the graphs with Hall index 2.

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