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List vertex arboricity of planar graphs without 5-cycles intersecting with 6-cycles
- Source :
- AIMS Mathematics, Vol 6, Iss 9, Pp 9757-9769 (2021)
- Publication Year :
- 2021
- Publisher :
- AIMS Press, 2021.
-
Abstract
- The vertex arboricity $ a(G) $ of a graph $ G $ is the minimum number of colors required to color the vertices of $ G $ such that no cycle is monochromatic. The list vertex arboricity $ a_l(G) $ is the list version of this concept. In this paper, we prove that if $ G $ is a planar graph without 5-cycles intersecting with 6-cycles, then $ a_l(G)\le 2 $.
Details
- Language :
- English
- ISSN :
- 24736988
- Volume :
- 6
- Issue :
- 9
- Database :
- OpenAIRE
- Journal :
- AIMS Mathematics
- Accession number :
- edsair.doi.dedup.....9f0a2db3d9ebad0eaf635e4660f7f6d7