Displaying similar documents to “An inductive proof of Whitney's Broken Circuit Theorem”

On the rooted Tutte polynomial

F. Y. Wu, C. King, W. T. Lu (1999)

Annales de l'institut Fourier

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The Tutte polynomial is a generalization of the chromatic polynomial of graph colorings. Here we present an extension called the rooted Tutte polynomial, which is defined on a graph where one or more vertices are colored with prescribed colors. We establish a number of results pertaining to the rooted Tutte polynomial, including a duality relation in the case that all roots reside around a single face of a planar graph.

Hypergraphs with Pendant Paths are not Chromatically Unique

Ioan Tomescu (2014)

Discussiones Mathematicae Graph Theory

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In this note it is shown that every hypergraph containing a pendant path of length at least 2 is not chromatically unique. The same conclusion holds for h-uniform r-quasi linear 3-cycle if r ≥ 2.

Mean value for the matching and dominating polynomial

Jorge Luis Arocha, Bernardo Llano (2000)

Discussiones Mathematicae Graph Theory

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The mean value of the matching polynomial is computed in the family of all labeled graphs with n vertices. We introduce the dominating polynomial of a graph whose coefficients enumerate the dominating sets for a graph and study some properties of the polynomial. The mean value of this polynomial is determined in a certain special family of bipartite digraphs.

On planar mixed hypergraphs.

Dvořák, Zdeněk, Král, Daniel (2001)

The Electronic Journal of Combinatorics [electronic only]

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M 2 -Edge Colorings Of Cacti And Graph Joins

Július Czap, Peter Šugerek, Jaroslav Ivančo (2016)

Discussiones Mathematicae Graph Theory

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An edge coloring φ of a graph G is called an M2-edge coloring if |φ(v)| ≤ 2 for every vertex v of G, where φ(v) is the set of colors of edges incident with v. Let 𝒦2(G) denote the maximum number of colors used in an M2-edge coloring of G. In this paper we determine 𝒦2(G) for trees, cacti, complete multipartite graphs and graph joins.