Path partition of planar graphs with girth at least six
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Published:2022-10-17
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Volume:
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ISSN:1793-8309
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Container-title:Discrete Mathematics, Algorithms and Applications
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language:en
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Short-container-title:Discrete Math. Algorithm. Appl.
Author:
Liu Xiaoling1,
Sun Lei1ORCID,
Zheng Wei1
Affiliation:
1. School of Mathematics and Statistics, Shandong Normal University, Jinan 250014, P. R. China
Abstract
A graph [Formula: see text] has a [Formula: see text]-partition if [Formula: see text] can be partitioned into two nonempty disjoint subsets [Formula: see text] and [Formula: see text] so that [Formula: see text] and [Formula: see text] are graphs whose components are paths of order at most [Formula: see text] and [Formula: see text], respectively. In this paper, we proved that every planar graph with girth at least six giving that [Formula: see text]-cycle is not intersecting with [Formula: see text]-cycle admits a [Formula: see text]-partition, where [Formula: see text] and [Formula: see text].
Funder
National Natural Science Foundation of China
Natural Science Foundation of Shandong Province
Publisher
World Scientific Pub Co Pte Ltd
Subject
Discrete Mathematics and Combinatorics