Abstract
If F, G and H are graphs, write F → (G, H) to mean that if the edges of F are colored red and blue, either a red G or a blue H must occur. It is shown that, if G and H are fixed 3-connected graphs (or triangles), then deciding whether F \(\not \to \) (G, H) is an NP-complete problem. On the other hand, if G and H are arbitrary stars, or if G is fixed matching and H is any fixed graph, the complexity of the problem is polynomial bounded.
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Burr, S.A. (1990). On the Computational Complexity of Ramsey—Type Problems. In: Nešetřil, J., Rödl, V. (eds) Mathematics of Ramsey Theory. Algorithms and Combinatorics, vol 5. Springer, Berlin, Heidelberg. https://doi.org/10.1007/978-3-642-72905-8_5
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DOI: https://doi.org/10.1007/978-3-642-72905-8_5
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