Best Monotone Degree Bounds for Various Graph Parameters
نویسندگان
چکیده
We identify best monotone degree bounds for the chromatic number and independence number of a graph. These bounds are best in the same sense as Chvátal’s hamiltonian degree condition. 1 Terminology and Notation We consider only undirected graphs without loops or multiple edges. Our terminology and notation will be standard except as indicated, and a good reference for any undefined terms is [14]. A degree sequence of a graph is any sequence π = (d1, d2, . . . , dn) consisting of the vertex degrees of the graph. We will usually assume the degree sequence is in nondecreasing order (in contrast to [14], where degree sequences are usually in nonincreasing order). We will generally use the standard abbreviated notation for degree sequences, e.g., (4, 4, 4, 4, 4, 5, 5) will be denoted 45. A sequence of integers π = (d1, . . . , dn) is called graphical if there exists a graph G having π as ∗Regretfully, Lou Hakimi died in June 2006.
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