Destroying Multicolored Paths and Cycles in Edge-Colored Graphs
Autor: | Eckstein, Nils Jakob, Grüttemeier, Niels, Komusiewicz, Christian, Sommer, Frank |
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Rok vydání: | 2021 |
Předmět: | |
Zdroj: | Discrete Mathematics & Theoretical Computer Science, vol. 25:1, Graph Theory (March 3, 2023) dmtcs:7636 |
Druh dokumentu: | Working Paper |
DOI: | 10.46298/dmtcs.7636 |
Popis: | We study the computational complexity of $c$-Colored $P_\ell$ Deletion and $c$-Colored $C_\ell$ Deletion. In these problems, one is given a $c$-edge-colored graph and wants to destroy all induced $c$-colored paths or cycles, respectively, on $\ell$ vertices by deleting at most $k$ edges. Herein, a path or cycle is $c$-colored if it contains edges of $c$ distinct colors. We show that $c$-Colored $P_\ell$ Deletion and $c$-Colored $C_\ell$ Deletion are NP-hard for each non-trivial combination of $c$ and $\ell$. We then analyze the parameterized complexity of these problems. We extend the notion of neighborhood diversity to edge-colored graphs and show that both problems are fixed-parameter tractable with respect to the colored neighborhood diversity of the input graph. We also provide hardness results to outline the limits of parameterization by the standard parameter solution size $k$. Finally, we consider bicolored input graphs and show a special case of $2$-Colored $P_4$ Deletion that can be solved in polynomial time. Comment: 31 pages |
Databáze: | arXiv |
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