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Some recent results on domination in graphs

100%

Plummer M.

Discussiones Mathematicae Graph Theory

2006

tom 26

nr 3

457-474

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.

On a special case of Hadwiger's conjecture

51%

Plummer M., Stiebitz M., Toft B.

Discussiones Mathematicae Graph Theory

2003

tom 23

nr 2

333-363

Hadwiger's Conjecture seems difficult to attack, even in the very special case of graphs G of independence number α(G) = 2. We present some results in this special case.

Ograniczanie wyników

2 Discussiones Mathematicae Graph Theory

2 Plummer M.

1 Stiebitz M.

1 Toft B.

1 2006

1 2003

Wyniki wyszukiwania

Some recent results on domination in graphs

On a special case of Hadwiger's conjecture