On low rank-width colorings
- Authors
- Kwon, O jung; Pilipczuk, Michal; Siebertz, Sebastian
- Issue Date
- Jan-2020
- Publisher
- ACADEMIC PRESS LTD- ELSEVIER SCIENCE LTD
- Citation
- EUROPEAN JOURNAL OF COMBINATORICS, v.83
- Indexed
- SCIE
SCOPUS
- Journal Title
- EUROPEAN JOURNAL OF COMBINATORICS
- Volume
- 83
- URI
- https://scholarworks.bwise.kr/hanyang/handle/2021.sw.hanyang/189310
- DOI
- 10.1016/j.ejc.2019.103002
- ISSN
- 0195-6698
- Abstract
- We introduce the concept of low rank-width colorings, generalizing the notion of low tree-depth colorings introduced by Nesetril and Ossona de Mendez (2008). We say that a class C of graphs admits low rank-width colorings if there exist functions N: N N and Q: N ( )-> N such that for all p is an element of N, every graph G is an element of C can be vertex colored with at most N(p) colors such that the union of any i <= p color classes induces a subgraph of rank-width at most Q(i).,Graph classes admitting low rank-width colorings strictly generalize graph classes admitting low tree-depth colorings and graph classes of bounded rank-width. We prove that for every graph class C of bounded expansion and every positive integer r, the class {G(r): G is an element of C}I of rth powers of graphs from' admits low rank-width colorings. On the negative side, we show that the classes of interval graphs and permutation graphs do not admit low rank-width colorings. As interesting side properties, we prove that every hereditary graph class admitting low rank-width colorings has the Erodos-Hajnal property and is chi-bounded.
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