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Pfaffian Graphs
, 2004
"... It is well known that, in general, the problem of determining the number of perfect matchings of a graph is NPhard. Some graphs, called Pfaffian, have a special type of orientation that is also called Pfaffian. Given a Pfaffian orientation of a graph G, the number of perfect matchings of G may b ..."
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It is well known that, in general, the problem of determining the number of perfect matchings of a graph is NPhard. Some graphs, called Pfaffian, have a special type of orientation that is also called Pfaffian. Given a Pfaffian orientation of a graph G, the number of perfect matchings of G may
On minimally nonPfaffian graphs
, 2007
"... We consider the question of characterizing Pfaffian graphs. We exhibit an infinite family of nonPfaffian graphs minimal with respect to the matching minor relation. This is in sharp contrast with bipartite case, as Little [7] proved that every bipartite nonPfaffian graph contains a matching minor ..."
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Cited by 1 (1 self)
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We consider the question of characterizing Pfaffian graphs. We exhibit an infinite family of nonPfaffian graphs minimal with respect to the matching minor relation. This is in sharp contrast with bipartite case, as Little [7] proved that every bipartite nonPfaffian graph contains a matching minor
Drawing Pfaffian graphs
 PROC. 12TH INT. SYMPOSIUM ON GRAPH DRAWING
, 2005
"... We prove that a graph is Pfaffian if and only if it can be drawn in the plane (possibly with crossings) so that every perfect matching intersects itself an even number of times. ..."
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Cited by 5 (3 self)
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We prove that a graph is Pfaffian if and only if it can be drawn in the plane (possibly with crossings) so that every perfect matching intersects itself an even number of times.
Drawing 4Pfaffian graphs on the torus
"... Abstract. We say that a graph G is kPfaffian if the generating function of its perfect matchings can be expressed as a linear combination of Pfaffians of k matrices corresponding to orientations of G. We prove that 3Pfaffian graphs are 1Pfaffian, 5Pfaffian graphs are 4Pfaffian and that a graph ..."
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Cited by 4 (0 self)
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Abstract. We say that a graph G is kPfaffian if the generating function of its perfect matchings can be expressed as a linear combination of Pfaffians of k matrices corresponding to orientations of G. We prove that 3Pfaffian graphs are 1Pfaffian, 5Pfaffian graphs are 4Pfaffian and that a graph
Towards a Characterisation of Pfaffian graphs
, 2008
"... A bipartite graph G is known to be Pfaffian if and only if it does not contain an even subdivision H of K3,3 such that G − V H contains a 1factor. However a general characterisation of Pfaffian graphs in terms of forbidden subgraphs is currently not known. In this paper we describe a possible app ..."
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Cited by 1 (1 self)
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A bipartite graph G is known to be Pfaffian if and only if it does not contain an even subdivision H of K3,3 such that G − V H contains a 1factor. However a general characterisation of Pfaffian graphs in terms of forbidden subgraphs is currently not known. In this paper we describe a possible
Pfaffian graphs, tjoins, and crossing numbers
"... Abstract. We prove a technical theorem about the numbers of crossings in Tjoins in different drawings of a fixed graph. As a corollary we characterize Pfaffian graphs in terms of their drawings in the plane and give a new proof of a theorem of Kleitman on the parity of crossings in drawings of K2j+ ..."
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Cited by 6 (0 self)
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Abstract. We prove a technical theorem about the numbers of crossings in Tjoins in different drawings of a fixed graph. As a corollary we characterize Pfaffian graphs in terms of their drawings in the plane and give a new proof of a theorem of Kleitman on the parity of crossings in drawings of K2j
PFAFFIAN LABELINGS AND SIGNS OF EDGE COLORINGS
 COMBINATORICA
, 2008
"... We relate signs of edgecolorings (as in classical Penrose’s result) with “Pfaffian labelings”, a generalization of Pfaffian orientations, whereby edges are labeled by elements of an Abelian group with an element of order two. In particular, we prove a conjecture of Goddyn that all kedgecolorings ..."
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edgecolorings of a kregular Pfaffian graph G have the same sign. We characterize graphs that admit a Pfaffian labeling in terms of bricks and braces in their matching decomposition and in terms of their drawings in the projective plane.
EMBEDDINGS OF PFAFFIAN BRACES AND POLYHEX GRAPHS
, 2009
"... Let G be a graph admitting a perfect matching. A cycle of even size C is central if G − C has a perfect matching. Given an orientation to G, an even cycle C is oddly oriented if along either direction of traversal around C, the number of edges of C with the direction as the same as the traversal di ..."
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direction is odd. An orientation of G is Pfaffian if every central cycle of G is oddly oriented. A graph G is Pfaffian if it has a Pfaffian orientation. In this paper, we show that every embedding of a Pfaffian brace on a surface with positive genus has facewidth at most three and that the cyclic edge
Results 1  10
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