Article ID | Journal | Published Year | Pages | File Type |
---|---|---|---|---|
5776970 | Discrete Mathematics | 2017 | 4 Pages |
Abstract
A path partition P of a digraph D is a set of disjoint paths which covers V(D). Let k be a positive integer. The k-norm of a path partition P of a digraph is defined as âPâPmin{|V(P)|,k}. Let Ïk(D) denote the smallest k-norm among all path partitions of a digraph D. In 1981, Linial conjectured that for any positive integer k each digraph D contains k disjoint stable sets whose union has size at least Ïk(D). We prove this conjecture for a class of digraphs we call spine digraphs, which is a proper generalization of split digraphs.
Keywords
Related Topics
Physical Sciences and Engineering
Mathematics
Discrete Mathematics and Combinatorics
Authors
Maycon Sambinelli, Cândida Nunes da Silva, Orlando Lee,