- Tytuł:
- WORM Colorings of Planar Graphs
- Autorzy:
-
Czap, J.
Jendrol’, S.
Valiska, J. - Tematy:
-
plane graph
monochromatic path
rainbow path
WORM coloring
facial coloring - Pokaż więcej
- Wydawca:
- Uniwersytet Zielonogórski. Wydział Matematyki, Informatyki i Ekonometrii
- Powiązania:
- https://bibliotekanauki.pl/articles/31341972.pdf Link otwiera się w nowym oknie
- Opis:
- Given three planar graphs $F$, $H$, and $G$, an $(F,H)$-WORM coloring of $G$ is a vertex coloring such that no subgraph isomorphic to $F$ is rainbow and no subgraph isomorphic to $H$ is monochromatic. If $G$ has at least one $(F,H)$-WORM coloring, then $ W_{F,H}^- (G)$ denotes the minimum number of colors in an $(F,H)$-WORM coloring of $G$. We show that (a) $W_{F,H}^- (G) \le 2 $ if $ |V (F)| \ge 3$ and $H$ contains a cycle, (b) $W_{F,H}^- (G) \le 3 $ if $ |V (F)| \ge 4$ and $H$ is a forest with $ \Delta (H) \ge 3$, (c) $W_{F,H}^- (G) \le 4 $ if $ |V (F)| \ge 5$ and $H$ is a forest with $1 \le \Delta (H) \le 2 $. The cases when both $F$ and $H$ are nontrivial paths are more complicated; therefore we consider a relaxation of the original problem. Among others, we prove that any 3-connected plane graph (respectively outerplane graph) admits a 2-coloring such that no facial path on five (respectively four) vertices is monochromatic.
- Dostawca treści:
- Biblioteka Nauki
Artykuł