Vertex-monochromatic connectivity of strong digraphs
Abstract
A vertex coloring of a strong digraph $D$ is a \emph{strong vertex-monochromatic connection coloring (SVMC-coloring)} if for every pair $u, v$ of vertices in $D$ there exists an $(u,v)$-path having all its internal vertices of the same color. Let $smc_v(D)$ denote the maximum number of colors used in an SVMC-coloring of a digraph $D$. In this paper we determine the value of $smc_v(D)$, whenever $D$ is the line digraph of a digraph. Also, if $T$ is a tournament, we give conditions to find the exact value of $smc_v(T)$.
- Publication:
-
arXiv e-prints
- Pub Date:
- February 2019
- DOI:
- 10.48550/arXiv.1902.10004
- arXiv:
- arXiv:1902.10004
- Bibcode:
- 2019arXiv190210004G
- Keywords:
-
- Mathematics - Combinatorics;
- 05C15;
- 05C20
- E-Print:
- submitted to Discrete Mathematicas