Let G(V , E) be a simple, undirected graph where V is the set of vertices and E is the set of edges. A b-dimensional cube is a Cartesian product I 1 ΓI 2 Γβ’ β’ β’ΓI b , where each I i is a closed interval of unit length on the real line. The cubicity of G, denoted by cub(G), is the minimum positive in
Mixed search number and linear-width of interval and split graphs
β Scribed by Fedor V. Fomin; Pinar Heggernes; Rodica Mihai
- Publisher
- John Wiley and Sons
- Year
- 2009
- Tongue
- English
- Weight
- 107 KB
- Volume
- 56
- Category
- Article
- ISSN
- 0028-3045
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π SIMILAR VOLUMES
Let x(G) and o(G) denote the chromatic number and clique number of a graph G. We prove that x can be bounded by a function of o for two well-known relatives of interval graphs. Multiple interval graphs (the intersection graphs of sets which can be written as the union of t closed intervals of a line
## Abstract The interval number of a graph __G__ is the least natural number __t__ such that __G__ is the intersection graph of sets, each of which is the union of at most __t__ intervals, denoted by __i__(__G__). Griggs and West showed that $i(G)\le \lceil {1\over 2} (d+1)\rceil $. We describe the
The interval number of a graph G, denoted i(G), is the least positive integer t such that G is the intersection graph of sets, each of which is the union of t compact real intervals. It is known that every planar graph has interval number at most 3 and that this result is best possible. We investiga