Boxicity of graphs with bounded degree
نویسندگان
چکیده
منابع مشابه
Boxicity of graphs with bounded degree
The boxicity of a graph G = (V,E) is the smallest k for which there exist k interval graphs Gi = (V,Ei), 1 ≤ i ≤ k, such that E = E1 ∩ . . . ∩ Ek. Graphs with boxicity at most d are exactly the intersection graphs of (axis-parallel) boxes in Rd. In this note, we prove that graphs with maximum degree ∆ have boxicity at most ∆2 + 2, which improves the previous bound of 2∆2 obtained by Chandran et...
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Boxicity of a graph H , denoted by box(H), is the minimum integer k such that H is an intersection graph of axis-parallel kdimensional boxes in R. In this paper, we show that for a line graph G of a multigraph, box(G) ≤ 2∆(⌈log 2 log 2 ∆⌉ + 3) + 1, where ∆ denotes the maximum degree of G. Since ∆ ≤ 2(χ−1), for any line graph G with chromatic number χ, box(G) = O(χ log 2 log 2 (χ)). For the d-di...
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ژورنال
عنوان ژورنال: European Journal of Combinatorics
سال: 2009
ISSN: 0195-6698
DOI: 10.1016/j.ejc.2008.10.003