The Two Ear Theorem on Matching-Covered Graphs
نویسندگان
چکیده
منابع مشابه
The Two Ear Theorem on Matching-Covered Graphs
We give a simple and short proof for the two ear theorem on matchingcovered graphs which is a well-known result of Lovász and Plummer. The proof relies only on the classical results of Tutte and Hall on the existence of perfect matching in (bipartite) graphs.
متن کاملEar-decompositions of matching covered graphs
We call a graph matching-covered if every line belongs to a perfect matching. We study the technique of "ear-decompositions" of such graphs. We prove that a non-bipartite matchingcovered graph contains K~ or K2@Ka (the triangular prism). Using this result, we give new characterizations of those graphs whose matching and covering numbers are equal. We apply these results to the theory of r-criti...
متن کاملOn Generalizations of Matching-covered Graphs
Structural results for extensions of matching-covered graphs are presented in this paper.
متن کاملA note on minimal matching covered graphs
A graph is called matching covered if for its every edge there is a maximum matching containing it. It is shown that minimal matching covered graphs contain a perfect matching.
متن کاملOn Perfect Matchings in Matching Covered Graphs
Let G be a matching-covered graph, i.e., every edge is contained in a perfect matching. An edge subsetX ofG is feasible if there exists two perfect matchingsM1 andM2 such that |M1∩X| 6≡ |M2∩X| (mod 2). Lukot’ka and Rollová proved that an edge subset X of a regular bipartite graph is not feasible if and only if X is switching-equivalent to ∅, and they further ask whether a non-feasible set of a ...
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ژورنال
عنوان ژورنال: Journal of Combinatorial Theory, Series B
سال: 1998
ISSN: 0095-8956
DOI: 10.1006/jctb.1998.1824