5 papers · 1 filter
Partitioning triangle-free planar graphs into a forest and a linear forest
Guanwu Liu, Rongxing Xu
Raspaud and Wang conjectured that every triangle-free planar graph can be vertex-partitioned into an independent set and a forest. Independently, Kawarabayashi and Thomassen also r…
The ratio monotonicity of Eulerian-type polynomials
Jun-Ying Liu, Guanwu Liu, Shi-Mei Ma +1
This paper is motivated by determining the location of modes of some unimodal Eulerian-type polynomials. The notion of ratio monotonicity was introduced by Chen-Xia when they inves…
Optimal bisections of directed graphs
Guanwu Liu, Jie Ma, Chunlei Zu
In this paper, motivated by a problem of Scott and a conjecture of Lee, Loh and Sudakov we consider bisections of directed graphs. We prove that every directed graph with arcs…
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 …
Partitioning digraphs with outdegree at least 4
Guanwu Liu, Xingxing Yu
Scott asked the question of determining such that if is a digraph with arcs and minimum outdegree then has a partition such that $\min\left…