Displaying similar documents to “On the theory of Pfaffian orientations. II: T -joins, k -cuts, and duality of enumeration.”

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 a generalization of perfect b -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 A f = β , where A 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 k -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 k 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...