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Intersection Dimension and Maximum Degree

Institution:	1. The Institute of Mathematical Sciences, Taramani, Chennai-600113, India;1. Technische Universität Chemnitz, Germany;2. Universidade Federal do Rio Grande do Sul, Porto Alegre, Brazil;1. University of Kaiserslautern (Department of Mathematics), Kaiserslautern, Germany;2. Université Blaise Pascal (Clermont-Ferrand II, LIMOS), BP 10125, 63173 Aubière Cedex, France;1. Network Dynamics and Simulation Science Laboratory, Virginia Bioinformatics Institute, Virginia Tech Blacksburg, VA 24061, USA;2. Department of Computer Science and Automation, Indian Institute of Science, Bangalore 560012, India

Abstract:	We show that the intersection dimension of graphs with respect to several hereditary properties can be bounded as a function of the maximum degree. As an interesting special case, we show that the circular dimension of a graph with maximum degree Δ is at most $O (Δ \frac{\log Δ}{\log \log Δ)}$ . We also obtain bounds in terms of treewidth.

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