Eslachi, C. and Johnson, M. (2004) 'Characterization of graphs with Hall number 2.', Journal of graph theory., 45 (2). pp. 81-100.
Hall's condition is a simple requirement that a graph G and list assignment L must satisfy if G is to have a proper L-colouring. The Hall number of G is the smallest integer m such that whenever the lists on the vertices each has size at least m and Hall's condition is satisfied a proper L-colouring exists. Hilton and P.D. Johnson introduced the parameter and showed that a graph has Hall number 1 if and only if every block is a clique. In this paper we give a forbidden-induced-subgraph characterization of graphs with Hall number 2.
|Keywords:||List coloring, Hall number, Choice number, Chromatic number.|
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|Publisher Web site:||http://dx.doi.org/10.1002/jgt.10154|
|Record Created:||07 Oct 2008|
|Last Modified:||08 Apr 2009 16:36|
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