Local rainbow colorings of hypergraphs
Zhenyu Li, Weichan Liu, Guowei Sun, Xia Wang, Shunan Wei

TL;DR
This paper extends rainbow coloring concepts to hypergraphs, establishing bounds on local rainbow coloring numbers and identifying hypergraphs with bounded or subpolynomial coloring numbers.
Contribution
It introduces the concept of local rainbow coloring for hypergraphs, provides upper bounds, characterizes hypergraphs with bounded numbers, and establishes lower bounds for complex cases.
Findings
Upper bound: $C_r(n, H)= O(n^{(h-r)/h} imes h^{2r + r/h})$
Hypergraphs with at most 3 edges have bounded local rainbow coloring numbers
For large hypergraphs, the local rainbow coloring number grows polynomially with $n$
Abstract
In this paper, we generalize the concepts related to rainbow coloring to hypergraphs. Specifically, an -local coloring is defined as a collection of edge-colorings, for each vertex in the complete -uniform hypergraph , with the property that for any copy of in , there exists at least one vertex in such that provides a rainbow edge-coloring of (i.e., no two edges in share the same color under ). The minimum number of colors required for this coloring is denoted as the local rainbow coloring number . We first establish an upper bound of the local rainbow coloring number for -uniform hypergraphs consisting of vertices, that is, . Furthermore, we identify a set of -uniform…
Peer Reviews
No public reviews on file for this paper yet. If you reviewed it on a platform where reviews are public (OpenReview, ICLR, NeurIPS, ICML), you can paste yours below so the community can read it here.
Videos
No videos yet. Explain this paper in a talk, walkthrough, or lecture? Add one.
Taxonomy
TopicsLimits and Structures in Graph Theory · Advanced Graph Theory Research · Graph Labeling and Dimension Problems
