NSD Total Choosability of Planar Graphs with Girth at Least Four

DOI

10.2991/msota-16.2016.18How to use a DOI?

Keywords

NSD total coloring; choosability; girth; planar graph

Abstract

A proper total k-coloring of a graph G is a mapping from V (G) E(G) to {1, k} such that no adjacent or incident elements in V (G) E(G) receive the same color. Let (u)denote the sum of the colors on the edges incident with the vertex u and the color on u. A proper total k-coloring of G is called neighbor sum distinguishing if (u) (v) for each edge uv E(G) Let Lz(z V(G E(G)) be a set of lists of integer numbers, each of size k. The smallest k for which for any specified collection of such lists, there exists a neighbor sum distinguishing total coloring using colors from Lz for each z V(G E(G) is called the neighbor sum distinguishing total choosability of G, and denoted by chT (G). In this paper, we prove that chT (G) (G)+3 for planar graphs with girth at least 4. This implies that Pilsniak and Wozniak' conjecture is true for any planar graphs with girth at least 4 and (G) 7.

Copyright

© 2017, the Authors. Published by Atlantis Press.

Open Access

This is an open access article distributed under the CC BY-NC license (http://creativecommons.org/licenses/by-nc/4.0/).

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TY  - CONF
AU  - Xue Han
AU  - Jihui Wang
AU  - Baojian Qiu
PY  - 2016/12
DA  - 2016/12
TI  - NSD Total Choosability of Planar Graphs with Girth at Least Four
BT  - Proceedings of 2016 International Conference on Modeling, Simulation and Optimization Technologies and Applications (MSOTA2016)
PB  - Atlantis Press
SP  - 78
EP  - 80
SN  - 2352-538X
UR  - https://doi.org/10.2991/msota-16.2016.18
DO  - 10.2991/msota-16.2016.18
ID  - Han2016/12
ER  -