Conflict-Free Colouring using Maximum Independent Set and Minimum Colouring
S.M.Dhannya, N.S. Narayanaswamy

TL;DR
This paper introduces a polynomial-time approach for conflict-free colouring of hypergraphs, linking it to maximum independent set and minimum colouring problems, and provides solutions for interval hypergraphs.
Contribution
It presents a novel reduction of conflict-free colouring to maximum independent set and characterizes the problem via co-occurrence graphs, solving an open problem for interval hypergraphs.
Findings
Polynomial-time algorithm for conflict-free colouring of interval hypergraphs.
Characterization of conflict-free colouring number through graph chromatic number.
Perfectness results for co-occurrence and conflict graphs.
Abstract
Given a hypergraph , the conflict-free colouring problem is to colour vertices of using minimum colours so that each hyperedge in sees a unique colour. We present a polynomial time reduction from the conflict-free colouring problem in hypergraphs to the maximum independent set problem in a class of simple graphs, which we refer to as \textit{conflict graphs}. We also present another characterization of the conflict-free colouring number in terms of the chromatic number of graphs in an associated family of simple graphs, which we refer to as \textit{co-occurrence graphs}. We present perfectness results for co-occurrence graphs and a special case of conflict graphs. Based on these results and a linear program that returns an integer solution in polynomial time, we obtain a polynomial time algorithm to compute a minimum conflict-free colouring of interval hypergraphs, thus…
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Taxonomy
TopicsAdvanced Graph Theory Research · Complexity and Algorithms in Graphs · Graph Labeling and Dimension Problems
