Results 1  10
of
14
A GallaiEdmondstype structure theorem for pathmatchings
, 2002
"... As a generalization of matchings, Cunningham and Geelen introduced the notion of pathmatchings. We give a structure theorem for pathmatchings which generalizes the fundamental GallaiEdmonds structure theorem for matchings. Our proof is purely combinatorial. ..."
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Cited by 7 (1 self)
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As a generalization of matchings, Cunningham and Geelen introduced the notion of pathmatchings. We give a structure theorem for pathmatchings which generalizes the fundamental GallaiEdmonds structure theorem for matchings. Our proof is purely combinatorial.
On Polyhedra Related to Even Factors
, 2003
"... As a common generalization of matchings and matroid intersection, W.H. Cunningham and J.F. Geelen introduced the notion of pathmatching, which they generalized even further by introducing even factors of weakly symmetric digraphs. Later, a purely combinatorial approach to even factors was given by ..."
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Cited by 5 (0 self)
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As a common generalization of matchings and matroid intersection, W.H. Cunningham and J.F. Geelen introduced the notion of pathmatching, which they generalized even further by introducing even factors of weakly symmetric digraphs. Later, a purely combinatorial approach to even factors was given by Gy. Pap and L. Szegõ, who showed that the maximum even factor problem remains tractable in the class of hardly symmetric digraphs. The present paper shows a direct polyhedral way to derive weighted integer minmax formulae generalizing those previous results.
The PathPacking Structure of Graphs
, 2003
"... We prove EdmondsGallai type structure theorems for Mader's edge and vertexdisjoint paths including also capacitated variants, and state a conjecture generalizing Mader's minimax theorems on path packings and Cunningham and Geelen's pathmatching theorem. ..."
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Cited by 3 (0 self)
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We prove EdmondsGallai type structure theorems for Mader's edge and vertexdisjoint paths including also capacitated variants, and state a conjecture generalizing Mader's minimax theorems on path packings and Cunningham and Geelen's pathmatching theorem.
A Polyhedral Approach to Even Factors
, 2003
"... Generalizing pathmatchings, W.H. Cunningham and J.F. Geelen introduced the notion of even factor in directed graphs. In weakly symmetric directed graphs they proved a minmax formula for the maximum cardinality even factor by algebraic method and also discussed a primaldual method for the weighted ..."
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Cited by 1 (1 self)
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Generalizing pathmatchings, W.H. Cunningham and J.F. Geelen introduced the notion of even factor in directed graphs. In weakly symmetric directed graphs they proved a minmax formula for the maximum cardinality even factor by algebraic method and also discussed a primaldual method for the weighted case. Later, Gy. Pap and L. Szegõ proved a simplified formula by purely combinatorial method and derived a GallaiEdmonds type structure theorem. In this paper, polyhedra related to even factors are considered, integrality and total dual integrality of these linear descriptions are proved directly, without using earlier unweighted results.
A Weighted Independent Even Factor Algorithm
 ROBIN CHRISTIAN, R. BRUCE RICHTER, ET AL.
, 2009
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On Factorizations Of Directed Graphs By Cycles
, 2004
"... In this paper we present a minmax theorem for a factorization problem in directed graphs. This extends the BergeTutte formula on matchings as well as formulas for the maximum even factor in weakly symmetric directed graphs and a factorization problem in undirected graphs. We also prove an exten ..."
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In this paper we present a minmax theorem for a factorization problem in directed graphs. This extends the BergeTutte formula on matchings as well as formulas for the maximum even factor in weakly symmetric directed graphs and a factorization problem in undirected graphs. We also prove an extension to the structural theorem of Gallai and Edmonds about a canonical set attaining minimum in the formula. The matching matroid can be generalized to this context: we get a matroidal description of the coverable node sets.