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math.CO2024
Backbone coloring for graphs with degree 4
Krzysztof Michalik, Krzysztof Turowski
The -backbone coloring of the graph with backbone is a graph-coloring problem in which we are given a graph and a subgraph , and we want to assign colors to verti…
math.CO2023
Edge coloring of products of signed graphs
Robert Janczewski, Krzysztof Turowski, Bartłomiej Wróblewski
In 2020, Behr defined the problem of edge coloring of signed graphs and showed that every signed graph can be colored using exactly or colors, where $Δ(G…
math.CO2023
The Game Chromatic Number of Complete Multipartite Graphs
Paweł Obszarski, Krzysztof Turowski, Hubert Zięba
In this paper we investigate the game chromatic number for complete multipartite graphs. Our results consist of two findings: (1) building on Dunn's strategies for equal-sized part…