$F$-WORM colorings: Results for 2-connected graphs
Csilla Bujt\'as, Zsolt Tuza

TL;DR
This paper investigates $F$-WORM colorings in graphs, establishing existence, computational complexity, and specific coloring properties for fixed 2-connected graphs, including NP-completeness results and constructions with large color gaps.
Contribution
It provides new existence results, complexity proofs, and coloring gap constructions for $F$-WORM colorings in graphs with fixed 2-connected graphs.
Findings
Existence of graphs with arbitrary minimum $F$-WORM colors
NP-completeness of deciding $F$-WORM colorability
Large gaps in possible $K_n$-WORM coloring numbers
Abstract
Given two graphs and , an -WORM coloring of is an assignment of colors to its vertices in such a way that no -subgraph of is monochromatic or rainbow. If has at least one such coloring, then it is called -WORM colorable and denotes the minimum possible number of colors. Here, we consider -WORM colorings with a fixed 2-connected graph and prove the following three main results: (1) For every natural number , there exists a graph which is -WORM colorable and ; (2) It is NP-complete to decide whether a graph is -WORM colorable; (3) For each , it is NP-complete to decide whether a graph satisfies . This remains valid on the class of -WORM colorable graphs of bounded maximum degree. For complete graphs with we also prove: (4) For each there exists a graph…
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Taxonomy
TopicsAdvanced Graph Theory Research · Graph Labeling and Dimension Problems · Limits and Structures in Graph Theory
