Generalizing D-graphs |
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Authors: | Arthur Busch Nathan Kahl |
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Affiliation: | a University of Dayton, USA b University of Akron, USA c Seton Hall University, USA |
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Abstract: | Let ω0(G) denote the number of odd components of a graph G. The deficiency of G is defined as def(G)=maxX⊆V(G)(ω0(G-X)-|X|), and this equals the number of vertices unmatched by any maximum matching of G. A subset X⊆V(G) is called a Tutte set (or barrier set) of G if def(G)=ω0(G-X)-|X|, and an extreme set if def(G-X)=def(G)+|X|. Recently a graph operator, called the D-graph D(G), was defined that has proven very useful in examining Tutte sets and extreme sets of graphs which contain a perfect matching. In this paper we give two natural and related generalizations of the D-graph operator to all simple graphs, both of which have analogues for many of the interesting and useful properties of the original. |
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Keywords: | Matching D-graph Tutte set Barrier set Extreme set |
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