Document Type
Lecture
Publication Date
10-23-2024
Abstract
Along-standing conjecture of Thomassen says that every longest cycle of a 3-connected graph has a chord. Thomassen (2018) proved that if G is 2-connected and cubic, then any longest cycle must have a chord. He also showed that if G is a 3-connected graph with minimum degree at least 4, then some of the longest cycles in G must have a chord. Zhang (1987) proved that if G is a 3-connected simple planar graph which is 3-regular or has minimum degree at least 4, then every longest cycle of G must have a chord. Recently, Li and Liu showed that if G is a 2-connected cubic graph and x,y are two distinct vertices of G, then every longest (x,y)-path of G contains at least one internal vertex whose neighbors are all in the path. In this paper, we study chords of longest cycles passing through a specified small set and generalize Thomassen’s and Zhang’s above results. We also extend the above-mentioned result of Li and Liu for 2-connected cubic graphs. This is joint work with Haidong Wu.
Relational Format
presentation
Recommended Citation
Zhang, Shunzhe, "Chords of longest cycles passing through a specified small set" (2024). Combinatorics Seminar. 5.
https://egrove.olemiss.edu/math_combinatorics/5
