Idioma:

Burling graphs, chromatic number, and orthogonal tree-decompositions

Felsner, Stefan ; Joret, Gwenaël ; Micek, Piotr ; Trotter, William T. ; Wiechert, Veit

Electronic notes in discrete mathematics, 2017-08, Vol.61, p.415-420 [Periódico revisado por pares]

Texto completo disponível

Citações Citado por

Título:
Burling graphs, chromatic number, and orthogonal tree-decompositions
Autor: Felsner, Stefan ; Joret, Gwenaël ; Micek, Piotr ; Trotter, William T. ; Wiechert, Veit
Assuntos: chromatic number ; path decompositions ; tree decompositions
É parte de: Electronic notes in discrete mathematics, 2017-08, Vol.61, p.415-420
Descrição: A classic result of Asplund and Grünbaum states that intersection graphs of axis-aligned rectangles in the plane are χ-bounded. This theorem can be equivalently stated in terms of path-decompositions as follows: There exists a function f:N→N such that every graph that has two path-decompositions such that each bag of the first decomposition intersects each bag of the second in at most k vertices has chromatic number at most f(k). Recently, Dujmović, Joret, Morin, Norin, and Wood asked whether this remains true more generally for two tree-decompositions. In this note we provide a negative answer: There are graphs with arbitrarily large chromatic number for which one can find two tree-decompositions such that each bag of the first decomposition intersects each bag of the second in at most two vertices. Furthermore, this remains true even if one of the two decompositions is restricted to be a path-decomposition. This is shown using a construction of triangle-free graphs with unbounded chromatic number due to Burling, which we believe should be more widely known.
Editor: Elsevier B.V
Idioma: Inglês

Voltar para lista de resultados

Anterior Resultado 2