Work

Partitioning Planar Graphs Without Specific Cycles into a Forest and a Disjoint Union of Paths

Year: 2025

Type: article

Abstract: In this paper, we show that if a planar graph G satisfies the following conditions: (i) none of its 3-faces is adjacent to a 6−-face, and (ii) none of its 4-faces is adjacent to a 5−-face, then V(G) can be partitioned into two subsets, each induces a forest, while one of the forests has maximum degree of at most 2. This result implies that every planar graph (i) with no chordal 7−-cycles, or (ii) with neither 4- nor 6-cycles, also admits such a partition.

Source: Axioms

DOI: 10.3390/axioms14040293

Authors: Pongpat Sittitrai, Keaitsuda Maneeruk Nakprasit, Keaitsuda Maneeruk Nakprasit, Kittikorn Nakprasit, Kittikorn Nakprasit

Institutions: Walailak University, Khon Kaen University, Centre of Excellence in Mathematics, Ministry of Higher Education, Science, Research and Innovation

Language: English

Topic: Advanced Graph Theory Research

Subfield: Computational Theory and Mathematics

Field: Computer Science

Domain: Physical Sciences

Open Access status: gold

Estimated APC paid: $2,896

Funder: Walailak University