Intersecting edge distinguishing colorings of hypergraphs
Karolina Okrasa, Pawe{\l} Rz\k{a}\.zewski

TL;DR
This paper introduces a hypergraph coloring framework for edge labelings that distinguish neighboring vertices by sets or multisets, providing probabilistic bounds and algorithms, with applications to graph labeling and hypergraph properties.
Contribution
It generalizes neighbor-distinguishing labelings to hypergraphs, offering new bounds, algorithms, and connections to hypergraph property B, with extensions to list coloring.
Findings
Established upper bounds for list colorings guaranteeing neighbor distinction
Developed a polynomial expected time randomized algorithm for hypergraph colorings
Connected edge labelings of bipartite graphs to hypergraph property B
Abstract
An edge labeling of a graph distinguishes neighbors by sets (multisets, resp.), if for any two adjacent vertices and the sets (multisets, resp.) of labels appearing on edges incident to and are different. In an analogous way we define total labelings distinguishing neighbors by sets or multisets: for each vertex, we consider labels on incident edges and the label of the vertex itself. In this paper we show that these problems, and also other problems of similar flavor, admit an elegant and natural generalization as a hypergraph coloring problem. An ieds-coloring (iedm-coloring, resp.) of a hypergraph is a vertex coloring, in which the sets (multisets, resp.) of colors, that appear on every pair of intersecting edges are different. We show upper bounds on the size of lists, which guarantee the existence of an ieds- or iedm-coloring, respecting these lists. The proof is…
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Taxonomy
TopicsGraph Labeling and Dimension Problems · Limits and Structures in Graph Theory · Advanced Graph Theory Research
