15 papers
A proof of Bickle's conjecture on collapsible graphs
Xingzhi Zhan
A graph is said to be -collapsible if has minimum degree and every non-null proper induced subgraph of has minimum degree less than In 2018, Bickle conjectu…
Counterexamples to a conjecture of Hoa on maximal non-Hamiltonian graphs
Xingzhi Zhan
A graph G is said to be maximal non-Hamiltonian if G is non-Hamiltonian, but is Hamiltonian for every nonedge of In 1994, Vu Dinh Hoa conjectured that if is a lo…
The maximum number of paths of a given length in a nonhamiltonian graph
Chengli Li, Xingzhi Zhan
In 1980, Paul Erdős posed the following problem: For every positive integer determine a nonhamiltonian graph of order having the maximum number of Hamilton paths. We solve…
The minimum number of detours in a connected graph of minimum degree three
Xining Liu, Pu Qiao, Xingzhi Zhan
A longest path in a graph is called a detour. Denote by the minimum number of detours in a connected graph with minimum degree and order and denote by th…
Weakly pancyclic vertices in dense nonbipartite graphs
Yurui Tang, Xingzhi Zhan
Let be a graph of girth and circumference A vertex of is called weakly pancyclic if lies on an -cycle for every integer with …
Every -connected -graph of order at least seven contains a pancyclic edge
Chengli Li, Xingzhi Zhan
A graph is called an -graph if any induced subgraph of of order has size at least An edge in a graph of order is called pancyclic if for every i…