Vector spaces and the Petersen graph.
de Carvalho, Marcelo H., Little, C.H.C. (2008)
The Electronic Journal of Combinatorics [electronic only]
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Displaying similar documents to “On the theory of Pfaffian orientations. II: -joins, -cuts, and duality of enumeration.”
Vector spaces and the Petersen graph.
Glossary of signed and gain graphs and allied areas.
Zaslavsky, Thomas (1998)
The Electronic Journal of Combinatorics [electronic only]
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Parity versions of 2-connectedness.
Little, C., Vince, A. (2006)
The Electronic Journal of Combinatorics [electronic only]
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On eulerian irregularity in graphs
Eric Andrews, Chira Lumduanhom, Ping Zhang (2014)
Discussiones Mathematicae Graph Theory
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A closed walk in a connected graph G that contains every edge of G exactly once is an Eulerian circuit. A graph is Eulerian if it contains an Eulerian circuit. It is well known that a connected graph G is Eulerian if and only if every vertex of G is even. An Eulerian walk in a connected graph G is a closed walk that contains every edge of G at least once, while an irregular Eulerian walk in G is an Eulerian walk that encounters no two edges of G the same number of times. The minimum...
On the number of dissimilar pfaffian orientations of graphs
Marcelo H. de Carvalho, Cláudio L. Lucchesi, U. S. R. Murty (2005)
RAIRO - Theoretical Informatics and Applications - Informatique Théorique et Applications
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On the theory of Pfaffian orientations. I: Perfect matchings and permanents.
Gallucio, Anna, Loebl, Martin (1999)
The Electronic Journal of Combinatorics [electronic only]
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A generalization of the dichromatic polynomial of a graph.
Farrell, E.J. (1981)
International Journal of Mathematics and Mathematical Sciences
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On a generalization of perfect -matching
Ľubica Šándorová, Marián Trenkler (1991)
Mathematica Bohemica
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The paper is concerned with the existence of non-negative or positive solutions to , where is the vertex-edge incidence matrix of an undirected graph. The paper gives necessary and sufficient conditions for the existence of such a solution.
The graph polynomial and the number of proper vertex coloring
Michael Tarsi (1999)
Annales de l'institut Fourier
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Alon and Tarsi presented in a previous paper a certain weighted sum over the set of all proper -colorings of a graph, which can be computed from its graph polynomial. The subject of this paper is another combinatorial interpretation of the same quantity, expressed in terms of the numbers of certain modulo flows in the graph. Some relations between graph parameters can be obtained by combining these two formulas. For example: The number of proper 3-colorings of a 4-regular graph and...