4 citations · 11 across the 18 of their papers we have counts for
7 papers · 1 filter
DP-4-colorability of two classes of planar graphs
Lily Chen, Runrun Liu, Gexin Yu +2
DP-coloring (also known as correspondence coloring) is a generalization of list coloring introduced recently by Dvořák and Postle (2017). In this paper, we prove that every planar…
Minimum degree condition for a graph to be knitted
Runrun Liu, Martin Rolek, Gexin Yu
For a positive integer , a graph is -knitted if for each -subset of vertices, and every partition of into disjoint parts for some , one…
DP-3-coloring of planar graphs without -cycles and two cycles from
Runrun Liu, Sarah Loeb, Martin Rolek +2
A generalization of list-coloring, now known as DP-coloring, was recently introduced by Dvořák and Postle. Essentially, DP-coloring assigns an arbitrary matching between lists of c…
Planar graphs without 4-cycles and close triangles are (2,0,0)-colorable
Heather Hoskins, Runrun Liu, Jennifer Vandenbussche +1
For a set of nonnegative integers , a -coloring of a graph is a partition of into such that for every , $…
Every planar graph without 4-cycles adjacent to two triangles is DP-4-colorable
Runrun Liu, Xiangwen Li
Wang and Lih in 2002 conjectured that every planar graph without adjacent triangles is 4-choosable. In this paper, we prove that every planar graph without any 4-cycle adjacent to…
Every planar graph without adjacent cycles of length at most is -choosable
Runrun Liu, Xiangwen Li
DP-coloring as a generalization of list coloring was introduced by Dvořák and Postle in 2017, who proved that every planar graph without cycles from 4 to 8 is 3-choosable, which wa…