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Bipartite knots

Sergei Duzhin, Mikhail Shkolnikov (2014)

Fundamenta Mathematicae

We give a solution to a part of Problem 1.60 in Kirby's list of open problems in topology, thus answering in the positive the question raised in 1987 by J. Przytycki.

Bipartition Polynomials, the Ising Model, and Domination in Graphs

Markus Dod, Tomer Kotek, James Preen, Peter Tittmann (2015)

Discussiones Mathematicae Graph Theory

This paper introduces a trivariate graph polynomial that is a common generalization of the domination polynomial, the Ising polynomial, the matching polynomial, and the cut polynomial of a graph. This new graph polynomial, called the bipartition polynomial, permits a variety of interesting representations, for instance as a sum ranging over all spanning forests. As a consequence, the bipartition polynomial is a powerful tool for proving properties of other graph polynomials and graph invariants....

Biplanes.

Peter J. Cameron (1973)

Mathematische Zeitschrift

Block decomposition approach to compute a minimum geodetic set

Tınaz Ekim, Aysel Erey (2014)

RAIRO - Operations Research - Recherche Opérationnelle

In this paper, we develop a divide-and-conquer approach, called block decomposition, to solve the minimum geodetic set problem. This provides us with a unified approach for all graphs admitting blocks for which the problem of finding a minimum geodetic set containing a given set of vertices (g-extension problem) can be efficiently solved. Our method allows us to derive linear time algorithms for the minimum geodetic set problem in (a proper superclass of) block-cacti and monopolar chordal graphs....

Boolean differential operators

Jorge Catumba, Rafael Díaz (2014)

Commentationes Mathematicae Universitatis Carolinae

We consider four combinatorial interpretations for the algebra of Boolean differential operators and construct, for each interpretation, a matrix representation for the algebra of Boolean differential operators.

Boolean graphs

Juhani Nieminen (1988)

Commentationes Mathematicae Universitatis Carolinae

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