42 citations · 153 across the 70 of their papers we have counts for
7 papers · 1 filter
The Alon-Tarsi number of planar graphs
Xuding Zhu
This paper proves that the Alon-Tarsi number of any planar graph is at most , which gives an alternate proof of the -choosability as well as the -paintability of planar gr…
List colouring of graphs and generalized Dyck paths
Rongxing Xu, Yeong-Nan Yeh, Xuding Zhu
The Catalan numbers occur in various counting problems in combinatorics. This paper reveals a connection between the Catalan numbers and list colouring of graphs. Assume is a g…
A note on two conjectures that strengthen the four colour theorem
Xuding Zhu
There are two conjectures concerning planar graph colourings that are strengthenings of the four colour theorem. One concerns signed graph colouring and is proposed by Máčajová, Ra…
Extremal problems on saturation for the family of -edge-connected graphs
Hui Lei, Suil O, Yongtang Shi +2
Let be a family of graphs. A graph is -saturated if contains no member of as a subgraph but contains some member of $\mathcal…
Defective 3-Paintability of Planar Graphs
Grzegorz Gutowski, Ming Han, Tomasz Krawczyk +1
A -defective -painting game on a graph is played by two players: Lister and Painter. Initially, each vertex is uncolored and has tokens. In each round, Lister marks a…
Total weight choosability for Halin graphs
Yu-Chang Liang, Tsai-Lien Wong, Xuding Zhu
A proper total weighting of a graph is a mapping which assigns to each vertex and each edge of a real number as its weight so that for any edge of , $\sum_{e \i…