For every fixed odd integer k at least 3 and all sufficiently large n, every graph on 2n+1 vertices with n squared plus n plus 1 edges contains two equal-degree vertices joined by a path of length k.
Title resolution pending
2 Pith papers cite this work. Polarity classification is still indexing.
2
Pith papers citing it
fields
math.CO 2years
2026 2verdicts
UNVERDICTED 2representative citing papers
K_{n,n+1} is the unique graph on 2n+1 vertices with at least n^2 + n edges avoiding equal-degree vertices at path distance 5, for all n >= 11.
citing papers explorer
-
A generalization of Erd\H{o}s-Hajnal problem on paths with equal-degree endpoints
For every fixed odd integer k at least 3 and all sufficiently large n, every graph on 2n+1 vertices with n squared plus n plus 1 edges contains two equal-degree vertices joined by a path of length k.
-
Paths of length five with equal-degree endpoints
K_{n,n+1} is the unique graph on 2n+1 vertices with at least n^2 + n edges avoiding equal-degree vertices at path distance 5, for all n >= 11.