Linial’s Conjecture for Arc-spine Digraphs


  • Lucas Rigo Yoshimura Universidade Federal de São Carlos - Campus Sorocaba
  • Maycon Sambinelli Universidade de São Paulo
  • Cândida Nunes da Silva Universidade Federal de São Carlos - Campus Sorocaba
  • Orlando Lee Universidade Estadual de Campinas



A path partition P of a digraph D is a collection of directed paths such that every vertex belongs to precisely one path. Given a positive integer k, the k-norm of a path partition P of D is defined as Sum (p in P) min{|p_i|, k}. A path partition of a minimum k-norm is called k-optimal and its k-norm is denoted by π_k(D). A stable set of a digraph D is a subset of pairwise non-adjacent
vertices of V(D). Given a positive integer k, we denote by alpha_k(D) the largest set of vertices of D that can be decomposed into k disjoint stable sets of D. In 1981, Linial conjectured that pi_k(D) ≤ alpha_k(D) for every digraph. We say that a digraph D is arc-spine if V(D) can be partitioned into two sets X and Y where X is traceable and Y contains at most one arc in A(D). In this paper we show the validity of Linial’s Conjecture for arc-spine digraphs.


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Como Citar

Rigo Yoshimura, L., Sambinelli, M., Nunes da Silva, C., & Lee, O. (2019). Linial’s Conjecture for Arc-spine Digraphs. Revista Eletrônica De Iniciação Científica Em Computação, 17(2).