5 papers
An exact formula for Erdős' problem 1005
Yanmohan Wang, Mingxu Xie, Ziyuan Zhao
In 1943, Erdős considered the minimum number of terms between two fractions in the Farey sequence of order whose numerators and denominators are oppositely ordered. Dete…
Longest cycles and Dirac-type results in highly connected graphs
Jie Ma, Bo Ning, Ziyuan Zhao
A classical theorem of Nash-Williams states that if is a -connected graph on vertices with minimum degree at least , then for every longest cycle of , th…
Dean's conjecture and cycles modulo k
Yufan Luo, Jie Ma, Ziyuan Zhao
Dean conjectured three decades ago that every graph with minimum degree at least contains a cycle whose length is divisible by . While the conjecture has been verified…
Intersections of longest cycles in vertex-transitive and highly connected graphs
Jie Ma, Ziyuan Zhao
Motivated by the classical conjectures of Lovász, Thomassen, and Smith, recent work has renewed interest in the study of longest cycles in important graph families, such as vertex-…
Leaf-to-leaf paths and cycles in degree-critical graphs
Francesco Di Braccio, Kyriakos Katsamaktsis, Jie Ma +2
An -vertex graph is degree 3-critical if it has edges and no proper induced subgraph with minimum degree at least 3. In 1988, Erdős, Faudree, Gyárfás, and Schelp asked…