List -coloring of sparse plane graphs.

Borodin, O.V.; Ivanova, A.O.; Neustroeva, T.K.

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Displaying similar documents to “List $(p, q)$ -coloring of sparse plane graphs.”

Sufficient conditions for the minimum 2-distance colorability of plane graphs of girth 6.

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We discuss possible topological configurations of nodal sets, in particular the number of their components, for spherical harmonics on $S^{2}$ . We also construct a solution of the equation $Δ u = u$ in $ℝ^{2}$ that has only two nodal domains. This equation arises in the study of high energy eigenfunctions.

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a-Weyl's theorem and the single valued extension property.

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Extracta Mathematicae

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In the present paper, we study a-Weyl's and a-Browder's theorem for an operator T such that T or T* satisfies the single valued extension property (SVEP). We establish that if T* has the SVEP, then T obeys a-Weyl's theorem if and only if it obeys Weyl's theorem. Further, if T or T* has the SVEP, we show that the spectral mapping theorem holds for the essential approximative point spectrum, and that a-Browder's theorem is satisfied by f(T) whenever f ∈ H(σ(T))....