Planar embeddability of the vertices of a graph using a fixed point set is NP-hard.

Cabello, Sergio

Displaying similar documents to “Planar embeddability of the vertices of a graph using a fixed point set is NP-hard.”

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Let Δ ≥ 4 be an integer. In this note, we prove that every planar graph with maximum degree Δ and girth at least 1 Δ+46 is strong (2Δ−1)-edgecolorable, that is best possible (in terms of number of colors) as soon as G contains two adjacent vertices of degree Δ. This improves [6] when Δ ≥ 6.

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Nonimprovable sufficient conditions for the solvability and unique solvability of the problem $u^{'} (t) = F (u) (t), u (a) - λ u (b) = h (u)$ are established, where $F : \to$ is a continuous operator satisfying the Carathèodory conditions, $h : \to R$ is a continuous functional, and $λ \in$ .

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