Chromatic number and minimum degree of Kr+1-free graphs
نویسنده
چکیده
Let (G) be the minimum degree of a graph G: A number of results about trianglefree graphs determine the maximum chromatic number of graphs of order n with (G) n=3: In this paper these results are extended to Kr+1-free graphs of order n with (G) (1 2= (2r 1))n: In particular: (a) there exist Kr+1-free graphs of order n with (G) > (1 2= (2r 1))n o (n) and arbitrary large chromatic number; (b) if G is a Kr+1-free graph of order n with (G) > (1 2= (2r 1))n; then (G) r + 2; (c) the structure of the (r + 1)-chromatic Kr+1-free graphs of order n; with (G) > (1 2=(2r 1)n is determined.
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