Year: 2026
Type: preprint
Abstract: Smith's conjecture asserts that in every $k$-connected graph with $k\geq 2$, any two longest cycles intersect in at least $k$ vertices. In this work, we establish an $Ω(k^{8/11})$ bound for this conjecture, improving upon the $Ω(k^{2/3})$ bound of Ma and Zhao. Our proof combines a Ramsey theoretic refinement of the traditional Turán-type approach with computer search.
Source: arXiv (Cornell University)
Author: Chen, Douglas M.
Language: English
Subfield: Discrete Mathematics and Combinatorics
Field: Mathematics
Domain: Physical Sciences
Open Access status: green
OpenAlex ID: W7204902894