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Bratislava, Slovakia

Kochol M.,MU SAV
Journal of Combinatorial Optimization | Year: 2016

We introduce canonical forms that represent certain equivalence classes of totally cyclic and acyclic orientations of graphs and present a polynomial algorithms for their constructions. The forms are used in new formulas evaluating tension and flow polynomials on graphs. © 2014, Springer Science+Business Media New York. Source


Kochol M.,MU SAV | Skrekovski R.,University of Ljubljana
Information Processing Letters | Year: 2012

The well-known Brooks Theorem says that each graph G of maximum degree k≥3 is k-colorable unless G=Kk+1. We generalize this theorem by allowing higher degree vertices with prescribed types of neighborhood. © 2011 Elsevier B.V. All rights reserved. Source


Kochol M.,MU SAV | Krivonakova N.,FPVzu | Smejova S.,FPVzu | Srankova K.,FPVzu
Information Processing Letters | Year: 2011

The 5-flow conjecture of Tutte is that every bridgeless graph has a nowhere-zero 5-flow. Recently Kochol developed a method giving lower bounds for the girth of a smallest counterexample to the 5-flow conjecture. It consists in comparing rank of a matrix with rank of its submatrix. In this paper we present a reduction of the size of these matrices. © 2010 Elsevier B.V. All rights reserved. Source


Kochol M.,MU SAV
Journal of Combinatorial Theory. Series B | Year: 2010

The famous 5-flow conjecture of Tutte is that every bridgeless graph has a nowhere-zero 5-flow. We show that a smallest counterexample to this conjecture must have girth at least eleven. © 2009 Elsevier Inc. Source


Kochol M.,MU SAV
Information Processing Letters | Year: 2012

We show that for each even m>2 and n≥4m-2, there exists a latin (n×n×(n-m))-parallelepiped that cannot be extended to a latin (n×n×(n-m+1))-parallelepiped. © 2012 Elsevier B.V. All rights reserved. Source

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