Flip colouring of graphs II
Xandru Mifsud

TL;DR
This paper investigates flip colourings in graphs, establishing conditions for their existence and constructing specific examples, while also exploring sequences of flip parameters with particular growth properties.
Contribution
It provides new existence results for (b,r)-flip graphs under certain bounds and analyzes the behavior of flip sequences over multiple steps.
Findings
Existence of (b,r)-flip graphs for certain b, r within specified bounds.
Construction of flip graphs with size proportional to b+r.
Analysis of flip sequences with unbounded growth over multiple steps.
Abstract
We give results concerning two problems on the recently introduced \textit{flip colourings of graphs}. For positive integers with , we say that a regular graph is a -\textit{flip graph} if there exists a red/blue edge colouring such that the red degree of every vertex is , the blue degree of every vertex is , yet in the closed neighbourhood of every vertex there are more blue edges than red edges. We prove that for integers with , small constructions of -flip graphs on vertices are possible. Furthermore, we prove that there exist -flip sequences where , such that can be arbitrarily large whilst is constant for .
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Taxonomy
TopicsLimits and Structures in Graph Theory · Coding theory and cryptography · Finite Group Theory Research
