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- W4300695957 abstract "Computing the clique number and chromatic number of a general graph are well-known NP-Hard problems. Codenotti et al. (Bruno Codenotti, Ivan Gerace, and Sebastiano Vigna. Hardness results and spectral techniques for combinatorial problems on circulant graphs. emph{Linear Algebra Appl.}, 285(1-3): 123--142, 1998) showed that computing clique number and chromatic number are still NP-Hard problems for the class of circulant graphs. We show that computing clique number is NP-Hard for the class of Cayley graphs for the groups $G^n$, where $G$ is any fixed finite group (e.g., cubelike graphs). We also show that computing chromatic number cannot be done in polynomial time (under the assumption $text{P}neq text{NP}$) for the same class of graphs. Our presentation uses free Cayley graphs. The proof combines free Cayley graphs with quotient graphs and Goppa codes." @default.
- W4300695957 created "2022-10-04" @default.
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- W4300695957 date "2015-02-03" @default.
- W4300695957 modified "2023-10-16" @default.
- W4300695957 title "Hardness of Computing Clique Number and Chromatic Number For Cayley Graphs" @default.
- W4300695957 doi "https://doi.org/10.48550/arxiv.1502.00965" @default.
- W4300695957 hasPublicationYear "2015" @default.
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