Work

A problem of Erdős and Hajnal on paths with equal-degree endpoints

Year: 2026

Type: article

Abstract: We address a problem posed by Erdős and Hajnal in 1991, proving that for all n ≥ 600 , every ( 2 n + 1 ) -vertex graph with at least n 2 + n + 1 edges contains two vertices of equal degree connected by a path of length three. The complete bipartite graph K n , n + 1 demonstrates that this edge bound is sharp. We further establish an analogous result for graphs with even order and investigate several related extremal problems.

Source: Journal of Combinatorial Theory Series B

DOI: 10.1016/j.jctb.2026.01.006

Authors: Kaizhe Chen, Jie Ma

Institutions: University of Science and Technology of China, Tsinghua University

Language: English

Topic: Limits and Structures in Graph Theory

Subfield: Discrete Mathematics and Combinatorics

Field: Mathematics

Domain: Physical Sciences

Open Access status: hybrid

Estimated APC paid: $4,150

Funders: National Natural Science Foundation of China, National Key Research and Development Program of China, National Key Research and Development Program of China Stem Cell and Translational Research