Alexandre A. Cezar

activity

20152020

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cs.DM2016

Circular Backbone Colorings: on matching and tree backbones of planar graphs

Julio Araujo, Fabricio Benevides, Alexandre Cezar +1

Given a graph $G$ , and a spanning subgraph $H$ of $G$ , a circular $q$ -backbone $k$ -coloring of $(G, H)$ is a proper $k$ -coloring $c$ of $G$ such that $q\le \lvert c(u)-c(v)\rvert \l…

cs.DM2015

On the Existence of Tree Backbones that Realize the Chromatic Number on a Backbone Coloring

Julio Araujo, Alexandre A. Cezar, Ana Silva

A proper $k$ -coloring of a graph $G = (V, E)$ is a function $c : V (G) \to {1, \dots, k}$ such that $c (u) \neq = c (v)$ , for every $uv \in E (G)$ . The chromatic number $χ (G)$ is the minimum $…