Monochromatic loose path partitions in k-uniform hypergraphs

2016/11/10 by Changhong Lü, Bing Wang, Lu, Changhong +3
Computer Science · Engineering · Mathematics · #Advanced Graph Theory Research #Combinatorics (math.CO) #FOS: Mathematics #Limits and Structures in Graph Theory #graph theory and CDMA systems

paper · pdf · doi:10.48550/arxiv.1611.03259

openalex publication_date 2016/11/10 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28

Abstract

A conjecture of Gyárfás and Sárközy says that in every 2-coloring of the edges of the complete k-uniform hypergraph K_n^k, there are two disjoint monochromatic loose paths of distinct colors such that they cover all but at most k-2 vertices. A weaker form of this conjecture with 2k-5 uncovered vertices instead of k-2 is proved, thus the conjecture holds for k=3. The main result of this paper states that the conjecture is true for all k≥ 3.

Related

• Monochromatic paths in 2-edge coloured graphs and hypergraphs
• Almost partitioning 2-coloured complete 3-uniform hypergraphs into two monochromatic tight or loose cycles
• On multicolor Ramsey numbers for loose k-paths of length three
• On monochromatic path covers conjecture of Erdős--Gyárfás
• Decompositions of edge-colored infinite complete graphs into monochromatic paths