Displaying similar documents to “Bounds for solutions of two additive equations of odd degree”

Arc-analyticity and polynomial arcs

Rémi Soufflet (2004)

Annales Polonici Mathematici

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We relate the notion of arc-analyticity and the one of analyticity on restriction to polynomial arcs and we prove that in the subanalytic setting, these two notions coincide.

On the dimension of additive sets

P. Candela, H. A. Helfgott (2015)

Acta Arithmetica

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We study the relations between several notions of dimension for an additive set, some of which are well-known and some of which are more recent, appearing for instance in work of Schoen and Shkredov. We obtain bounds for the ratios between these dimensions by improving an inequality of Lev and Yuster, and we show that these bounds are asymptotically sharp, using in particular the existence of large dissociated subsets of {0,1}ⁿ ⊂ ℤⁿ.

Rainbow Connectivity of Cacti and of Some Infinite Digraphs

Jesús Alva-Samos, Juan José Montellano-Ballesteros (2017)

Discussiones Mathematicae Graph Theory

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An arc-coloured digraph D = (V,A) is said to be rainbow connected if for every pair {u, v} ⊆ V there is a directed uv-path all whose arcs have different colours and a directed vu-path all whose arcs have different colours. The minimum number of colours required to make the digraph D rainbow connected is called the rainbow connection number of D, denoted rc⃗ (D). A cactus is a digraph where each arc belongs to exactly one directed cycle. In this paper we give sharp upper and lower bounds...

The arc-width of a graph.

Barát, János, Hajnal, Péter (2001)

The Electronic Journal of Combinatorics [electronic only]

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