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Critical concepts in domination. (English) Zbl 0725.05049

[For the entire collection see Zbl 0716.00005.]
The paper studies domination critical and domination perfect graphs. A graph is domination critical, if its domination number is k and decreases after adding any new edge. A graph is domination perfect, if the domination number of any of its subgraphs is equal to its independent domination number, i.e. the minimum number of vertices of a set which is simultaneously independent and dominating in G. Various properties of 3- critical graphs are described; degree sequences and diameters of such graphs are investigated. At the end some theorems on domination perfect graphs are proved, among them a theorem characterizing planar domination perfect graphs by means of forbidden induced subgraphs.

MSC:

05C35 Extremal problems in graph theory

Citations:

Zbl 0716.00005
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References:

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