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2017 | 37 | 2 | 315-336
Tytuł artykułu

Forbidden Structures for Planar Perfect Consecutively Colourable Graphs

Treść / Zawartość
Warianty tytułu
Języki publikacji
EN
Abstrakty
EN
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 subgraphs are consecutively colourable, too. We call elements of this class perfect consecutively colourable to emphasise the conceptual similarity to perfect graphs. Obviously, the class of perfect consecutively colourable graphs is induced hereditary, so it can be characterized by the family of induced forbidden graphs. In this work we give a necessary and sufficient conditions that must be satisfied by the generalized Sevastjanov rosette to be an induced forbid- den graph for the class of perfect consecutively colourable graphs. Along the way, we show the exact values of the deficiency of all generalized Sevastjanov rosettes, which improves the earlier known estimating result. It should be mentioned that the deficiency of a graph measures its closeness to the class of consecutively colourable graphs. We motivate the investigation of graphs considered here by showing their connection to the class of planar perfect consecutively colourable graphs.
Wydawca
Rocznik
Tom
37
Numer
2
Strony
315-336
Opis fizyczny
Daty
wydano
2017-05-01
otrzymano
2016-04-19
poprawiono
2016-10-01
zaakceptowano
2016-10-01
online
2017-04-01
Twórcy
Bibliografia
Typ dokumentu
Bibliografia
Identyfikatory
Identyfikator YADDA
bwmeta1.element.doi-10_7151_dmgt_1958
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