We establish relations between the bandwidth and the treewidth of bounded degree graphs G, and relate these parameters to the size of a separator of G as well as the size of an expanding subgraph of G. Our results imply that if one of these parameters is sublinear in the number of vertices of G then so are all the others. This implies for example that graphs of fixed genus have sublinear bandwidth or, more generally, a corresponding result for graphs with any fixed forbidden minor. As a consequence we establish a simple criterion for universality for such classes of graphs and show for example that for each gamma>0 every n-vertex graph with minimum degree ((3/4)+gamma)n contains a copy of every bounded-degree planar graph on n vertices if n is sufficiently large.
Institute for Basic Science（基础科学研究所）；Simon Fraser University（西蒙菲莎大学）；Charles University（查理大学）；Technical University of Denmark（丹麦技术大学）；Monash University（莫纳什大学）
Moderately beyond clique-width: reduced component max-leaf and related parameters
Univ Lyon, CNRS, ENS de Lyon, Université Claude Bernard Lyon 1（里昂大学、法国国家科学研究中心、巴黎高等师范学院里昂分校、克洛德·贝尔纳里昂大学）；Institute of Informatics, University of Warsaw（华沙大学信息学研究所）；Department of Mathematics and Research Institute for Natural Sciences, Hanyang University（汉阳大学数学系与自然科学研究所）；Discrete Mathematics Group, Institute for Basic Science (IBS)（基础科学研究院离散数学组）
