Intersection dimension and graph invariants | Zendy

N. R. Aravind | Zendy; C. R. Subramanian | Zendy

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Intersection dimension and graph invariants

Author(s) -

N. R. Aravind,

C. R. Subramanian

Publication year - 2018

Publication title -

discussiones mathematicae graph theory

Language(s) - English

Resource type - Journals

SCImago Journal Rank - 0.476

H-Index - 19

eISSN - 2083-5892

pISSN - 1234-3099

DOI - 10.7151/dmgt.2173

Subject(s) - mathematics , combinatorics , treewidth , intersection graph , bounded function , dimension (graph theory) , graph , intersection (aeronautics) , degree (music) , discrete mathematics , line graph , pathwidth , mathematical analysis , physics , acoustics , engineering , aerospace engineering

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(ΔlogΔlog logΔ) O\left( {\Delta {{\log \Delta } \over {\log \,\log \Delta }}} \right) . 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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