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Even Factors, Jump Systems, and Discrete Convexity
, 2007
"... A jump system, which is a set of integer lattice points with an exchange property, is an extended concept of a matroid. Some combinatorial structures such as the degree sequences of the matchings in an undirected graph are known to form a jump system. On the other hand, the maximum even factor probl ..."
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Cited by 7 (3 self)
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A jump system, which is a set of integer lattice points with an exchange property, is an extended concept of a matroid. Some combinatorial structures such as the degree sequences of the matchings in an undirected graph are known to form a jump system. On the other hand, the maximum even factor problem is a generalization of the maximum matching problem into digraphs. When the given digraph has a certain property called oddcyclesymmetry, this problem is polynomially solvable. The main result of this paper is that the degree sequences of all even factors in a digraph form a jump system if and only if the digraph is oddcyclesymmetric. Furthermore, as a generalization, we show that the weighted even factors induce Mconvex (Mconcave) functions on jump systems. These results suggest that even factors are a natural generalization of matchings and the assumption of oddcyclesymmetry of digraphs is essential.
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.
A partially ordered structure and a generalization of the canonical partition for general graphs with perfect matchings
 In: Proceedings of The 23rd International Symposium on Algorithms and Computation (ISAAC
, 2012
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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.