Year: 2026
Type: preprint
Abstract: Given $r \in \mathbb{N}$ and an edge-coloured complete graph such that the average number of colours incident with a vertex is at most $r$, Conlon and Stein asked whether there is a vertex partition into a bounded number of monochromatic cycles, and proved this for $r=2$. We settle the first open case by proving the corresponding statement for $r=3$.
Source: arXiv (Cornell University)
Language: English
Subfield: Discrete Mathematics and Combinatorics
Field: Mathematics
Domain: Physical Sciences
Open Access status: green
Awards: G1175115578, G168758689, G1705834326, G1939838603, G2148579211, G2262748287, G2382844429, G294895050, G300979063, Classical, asymptotic, quantum and geometric combinatorics, G3309460457, G3480869486, G3913422846, G4156530268, G425668148, G4608934693, G464105488, G4663050289, G4728539003, G5080475149, G6738675468, G6739720741, G6812024786, G701669800, G7084143925, G7958123509, Ramsey Theory: from monochromatic to canonical structures, G863151887
OpenAlex ID: W7172321788