On graphs having maximal independent sets of exactly $t$ distinct cardinalities

Details On graphs having maximal independent sets of exactly $t$ distinct cardinalities On graphs having maximal independent sets of exactly $t$ distinct cardinalities

2011-10-19

arxiv.org/abs/1110.4310v1

Mathematics

Combinatorics

8 pages, 2 figures

Scientific paper

For a given positive integer t we consider graphs having maximal independent
sets of precisely t distinct cardinalities and restrict our attention to those
that have no vertices of degree one. In the situation when t is four or larger
and the length of the shortest cycle is at least 6t-6, we completely
characterize such graphs.

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