Aravind, N.R. and Subramanian, C.R.
(2021)
Intersection dimension and graph invariants.
Discussiones Mathematicae Graph Theory, 41 (1).
p. 153.
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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