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Forbidden Structures for Planar Perfect Consecutively Colourable Graphs

Marta Borowiecka-Olszewska, Ewa Drgas-Burchardt (2017)

Discussiones Mathematicae Graph Theory

A consecutive colouring of a graph is a proper edge colouring with posi- tive integers in which the colours of edges incident with each vertex form an interval of integers. The idea of this colouring was introduced in 1987 by Asratian and Kamalian under the name of interval colouring. Sevast- janov showed that the corresponding decision problem is NP-complete even restricted to the class of bipartite graphs. We focus our attention on the class of consecutively colourable graphs whose all induced...

Functigraphs: An extension of permutation graphs

Andrew Chen, Daniela Ferrero, Ralucca Gera, Eunjeong Yi (2011)

Mathematica Bohemica

Let G 1 and G 2 be copies of a graph G , and let f : V ( G 1 ) V ( G 2 ) be a function. Then a functigraph C ( G , f ) = ( V , E ) is a generalization of a permutation graph, where V = V ( G 1 ) V ( G 2 ) and E = E ( G 1 ) E ( G 2 ) { u v : u V ( G 1 ) , v V ( G 2 ) , v = f ( u ) } . In this paper, we study colorability and planarity of functigraphs.

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