Some recent results on domination in graphs

• Autorzy: Michael D. Plummer
• Języki publikacji: EN

Abstrakty

EN

In this paper, we survey some new results in four areas of domination in graphs, namely:
(1) the toughness and matching structure of graphs having domination number 3 and which are "critical" in the sense that if one adds any missing edge, the domination number falls to 2;
(2) the matching structure of graphs having domination number 3 and which are "critical" in the sense that if one deletes any vertex, the domination number falls to 2;
(3) upper bounds on the domination number of cubic graphs; and
(4) upper bounds on the domination number of graphs embedded in surfaces.

Słowa kluczowe

EN

domination; matching; toughness; cubic graph; triangulation; genus

Kategorie tematyczne

• 05C70: Factorization, matching, partitioning, covering and packing
• 05C10: Planar graphs; geometric and topological aspects of graph theory
• 05C69: Dominating sets, independent sets, cliques

• Wydawca: De Gruyter Open
• Czasopismo: Discussiones Mathematicae Graph Theory
• Rocznik: 2006
• Tom: 26
• Numer: 3
• Strony: 457-474

Daty

wydano

2006

otrzymano

2005-11-23

Twórcy

autor

Michael D. Plummer

• Department of Mathematics, Vanderbilt University, Nashville, Tennessee 37240, USA

Bibliografia

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Identyfikatory

DOI

10.7151/dmgt.1338