Structural results on maximal k-degenerate graphs

• Autorzy: Allan Bickle
• Języki publikacji: EN

Abstrakty

EN

A graph is k-degenerate if its vertices can be successively deleted so that when deleted, each has degree at most k. These graphs were introduced by Lick and White in 1970 and have been studied in several subsequent papers. We present sharp bounds on the diameter of maximal k-degenerate graphs and characterize the extremal graphs for the upper bound. We present a simple characterization of the degree sequences of these graphs and consider related results. Considering edge coloring, we conjecture that a maximal k-degenerate graph is class two if and only if it is overfull, and prove this in some special cases. We present some results on decompositions and arboricity of maximal k-degenerate graphs and provide two characterizations of the subclass of k-trees as maximal k-degenerate graphs. Finally, we define and prove a formula for the Ramsey core numbers.

Słowa kluczowe

EN

k-degenerate; k-core; k-tree; degree sequence; Ramsey number

Kategorie tematyczne

• 05C75: Structural characterization of families of graphs

• Wydawca: De Gruyter Open
• Czasopismo: Discussiones Mathematicae Graph Theory
• Rocznik: 2012
• Tom: 32
• Numer: 4
• Strony: 659-676

Daty

wydano

2012

otrzymano

2011-06-09

poprawiono

2011-12-13

zaakceptowano

2011-12-13

Twórcy

autor

Allan Bickle

• Department of Mathematics, Western Michigan University, 1903 W. Michigan, Kalamazoo, MI 49008

Bibliografia

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Identyfikatory

DOI

10.7151/dmgt.1637