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…