Linear layouts measuring neighbourhoods in graphs

Autor: Frank Gurski
Rok vydání: 2006
Předmět:
Zdroj: Discrete Mathematics. 306(15):1637-1650
ISSN: 0012-365X
DOI: 10.1016/j.disc.2006.03.048
Popis: In this paper we introduce the graph layout parameter neighbourhood-width as a variation of the well-known cut-width. The cut-width of a graph G=(V,E) is the smallest integer k, such that there is a linear layout ϕ:V→{1,…,|V|}, such that for every 1⩽ii. The neighbourhood-width of a graph is the smallest integer k, such that there is a linear layout ϕ, such that for every 1⩽ii.We show that the neighbourhood-width of a graph differs from its linear clique-width or linear NLC-width at most by one. This relation is used to show that the minimization problem for neighbourhood-width is NP-complete.Furthermore, we prove that simple modifications of neighbourhood-width imply equivalent layout characterizations for linear clique-width and linear NLC-width.We also show that every graph of path-width k or cut-width k has neighbourhood-width at most k+2 and we give several conditions such that graphs of bounded neighbourhood-width have bounded path-width or bounded cut-width.
Databáze: OpenAIRE