β Scribed by Raymond J. Huntington
No coin nor oath required. For personal study only.
π SIMILAR VOLUMES
The interval number of a simple undirected graph G, denoted i(G), is the least nonnegative integer r for which we can assign to each vertex in G a collection of at most r intervals on the real line such that two distinct vertices u and w of G are adjacent if and only if some interval for u intersect
The interval number of a (simple, undirected) graph G is the least positive integer t such that G is the intersection graph of sets, each of which is the union of t real intervals. A chordal (or triangulated) graph is one with no induced cycles on 4 or more vertices. If G is chordal and has maximum
Three results on the interval number of a graph on n vertices are presented. (1) The interval number of almost every graph is between n/4 Ig n and n/4 (this also holds for almost every bipartite graph). ( 2) There exist K+\_,, -free bipartite graphs with interval number at least c(m)n 1-2'Cm+1J/lg