Maximal and Maximum Independent Sets In Graphs With At Most r Cycles
Combinatorics
2007-05-23 v1
Abstract
Let m(G) denote the number of maximal independent sets of vertices in a graph G and let c(n,r) be the maximum value of m(G) over all connected graphs with n vertices and at most r cycles. A theorem of Griggs, Grinstead, and Guichard gives a formula for c(n,r) when r is large relative to n, while a theorem of Goh, Koh, Sagan, and Vatter does the same when r is small relative to n. We complete the determination of c(n,r) for all n and r and characterize the extremal graphs. Problems for maximum independent sets are also completely resolved.
Keywords
Cite
@article{arxiv.math/0505048,
title = {Maximal and Maximum Independent Sets In Graphs With At Most r Cycles},
author = {Bruce E. Sagan and V. Vatter},
journal= {arXiv preprint arXiv:math/0505048},
year = {2007}
}
Comments
30 pages, 9 figures, Latex, see related papers at http://www.math.msu.edu/~sagan