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math.CO2022★ 2 cited
Odd coloring of 2-boundary planar graphs and beyond
Weichan Liu, Mengke Qi, Xin Zhang
In this paper, we introduce the notion of 2-boundary planar graphs. A graph is 2-boundary planar if it has an embedding in the plane so that all vertices lie on the boundary of at…
math.CO2022
Defective incidence coloring of graphs
Huimin Bi, Xin Zhang
We define the -defective incidence chromatic number of a graph, generalizing the notion of incidence chromatic number, and determine it for some classes of graphs including tree…
math.CO2022
Conflict-free incidence coloring of outer-1-planar graphs
Mengke Qi, Xin Zhang
An incidence of a graph is a vertex-edge pair such that is incidence with . A conflict-free incidence coloring of a graph is a coloring of the incidences in such…