Intersection dimension and graph invariants

Aravind, N R and Subramanian, C.R. (2020) Intersection dimension and graph invariants. Discussiones Mathematicae Graph Theory, 41 (1). pp. 153-166. ISSN 1234-3099

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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 Δis at most O(ΔlogΔ/log logΔ) . It is also shown that permutation dimension of any graph is at most Δ(log Δ)1+o(1). We also obtain bounds on intersection dimension in terms of treewidth.

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