List-recoloring of two classes of planar graphs
Chenran Pan, Weifan Wang, Runrun Liu

TL;DR
This paper proves that for certain classes of planar graphs and graphs with bounded average degree, there exists an efficient recoloring sequence between two list colorings, with each vertex recolored only a constant number of times.
Contribution
It extends previous theorems by establishing bounded recoloring sequences for specific classes of planar graphs and graphs with bounded average degree.
Findings
Recoloring sequences exist with each vertex recolored a constant number of times.
Results apply to planar graphs with no 3-cycles or intersecting 4-cycles, and to graphs with mad(G) < 5/2.
Strengthens earlier theorems by Cranston.
Abstract
For a graph with a list assignment and two -colorings and , an -recoloring sequence from to is a sequence of proper -colorings where consecutive colorings differ at exactly one vertex. We prove the existence of such a recoloring sequence in which every vertex is recolored at most a constant number of times under two conditions: (i) is planar, contains no -cycles or intersecting -cycles, and is a -assignment; or (ii) the maximum average degree of satisfies and is a -assignment. These results strengthen two theorems previously established by Cranston.
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Taxonomy
TopicsAdvanced Graph Theory Research · Limits and Structures in Graph Theory · Scheduling and Timetabling Solutions
