3 citations · 4 across the 7 of their papers we have counts for
7 papers
Improved bounds on the oriented diameter of planar triangulations
Xiaonan Liu
The oriented diameter of a connected bridgeless graph , denoted by , is the minimum diameter among all strong orientations of . We st…
Reconstruction and Edge Reconstruction of Triangle-free Graphs
Alexander Clifton, Xiaonan Liu, Reem Mahmoud +1
The Reconstruction Conjecture due to Kelly and Ulam states that every graph with at least 3 vertices is uniquely determined by its multiset of subgraphs . Let $…
Planar Turán Numbers of Cycles: A Counterexample
Daniel W. Cranston, Bernard Lidický, Xiaonan Liu +1
The planar Turan number is the largest number of edges in an -vertex planar graph with no -cycle. For , upper…
Polynomial -binding functions for -broom-free graphs
Xiaonan Liu, Joshua Schroeder, Zhiyu Wang +1
For any positive integer , a \emph{-broom} is a graph obtained from by subdividing an edge once. In this paper, we show that, for graphs without induced -b…
Counting Hamiltonian cycles in planar triangulations
Xiaonan Liu, Zhiyu Wang, Xingxing Yu
Hakimi, Schmeichel, and Thomassen in 1979 conjectured that every -connected planar triangulation on vertices has at least Hamiltonian cycles, with equality…
Number of Hamiltonian cycles in planar triangulations
Xiaonan Liu, Xingxing Yu
Whitney proved in 1931 that 4-connected planar triangulations are Hamiltonian. Hakimi, Schmeichel, and Thomassen conjectured in 1979 that if is a 4-connected planar triangulati…
Hamiltonian paths and cycles in some 4-uniform hypergraphs
Guanwu Liu, Xiaonan Liu
In 1999, Katona and Kierstead conjectured that if a -uniform hypergraph on vertices has minimum co-degree , i.e., each set of …