A ug 2 00 3 Short Cycles Connectivity

A ug 2 00 1 Derivatives of p - adic L - functions , Heegner cycles and monodromy modules attached to modular forms

Short Cycles Connectivity

Short cycles connectivity is a generalization of ordinary connectivity. Instead by a path (sequence of edges), two vertices have to be connected by a sequence of short cycles, in which two adjacent cycles have at least one common vertex. If all adjacent cycles in the sequence share at least one edge, we talk about edge short cycles connectivity. It is shown that the short cycles connectivity is...

ar X iv : m at h / 05 08 06 6 v 1 [ m at h . N T ] 3 A ug 2 00 5 MULTIPLE POLYLOGARITHMS , POLYGONS , TREES AND ALGEBRAIC CYCLES

We construct, for a field F and a natural number n, algebraic cycles in Bloch's cubical cycle group of codimension n cycles in P 1 F \{1} 2n−1 , which correspond to weight n multiple polylogarithms with generic arguments if F ⊂ C. Moreover, we construct out of them a Hopf subalgebra in the Bloch-Kriz cycle Hopf algebra χ cycle. In the process, we are led to other Hopf algebras built from trees ...

A ug 2 00 9 HAMILTON DECOMPOSITIONS OF REGULAR TOURNAMENTS

We show that every sufficiently large regular tournament can almost completely be decomposed into edge-disjoint Hamilton cycles. More precisely, for each η > 0 every regular tournament G of sufficiently large order n contains at least (1/2 − η)n edge-disjoint Hamilton cycles. This gives an approximate solution to a conjecture of Kelly from 1968. Our result also extends to almost regular tournam...

A ug 2 00 5 RAINBOW HAMILTON CYCLES IN RANDOM REGULAR GRAPHS SVANTE JANSON

A rainbow subgraph of an edge-coloured graph has all edges of distinct colours. A random d-regular graph with d even, and having edges coloured randomly with d/2 of each of n colours, has a rainbow Hamilton cycle with probability tending to 1 as n → ∞, provided d ≥ 8.