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Published in:
1990 | OriginalPaper | Chapter
Extending Hall’s Theorem
Authors : A. J. W. Hilton, P. D. Johnson Jr.
Published in: Topics in Combinatorics and Graph Theory
Publisher: Physica-Verlag HD
Included in: Professional Book Archive
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Let G be a finite simple graph. Suppose that to each vertex v ∈ V(G) there is assigned a finite set (or “list”) C(v) of colours (or “symbols”). The general problem is: what conditions on G and the colour-set assignment C guarantee that the vertices of G can be coloured so that each v ∈ V(G) is coloured with a colour from C(v), and adjacent vertices are coloured differently? Such a colouring of V(G) will be called a C-colouring of G.