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On the integrability of polynomial fields in the plane by means of Picard-Vessiot theory
Differential Galois Theory Darboux theory of Integrability Poincar´ e problem,
2011/2/24
We study the integrability of polynomial vector fields using Galois theory of linear differential equations when the associated foliations is reduced to a Riccati type folia-tion.
In this paper, we prove that every plane graph without 5-circuits and without triangles of distance less than 3 is 3-colorable. This improves the main result of Borodin and Raspaud [Borodin, O. V., Ra...