17 citations · 44 across the 18 of their papers we have counts for
5 papers · 1 filter
Counting cycles and finite dimensional Lp norms
Igor Rivin
We obtain sharp bounds for the number of n--cycles in a finite graph as a function of the number of edges, and prove that the complete graph is optimal in more ways than could be i…
Extremal metrics on graphs I
Dmitry Jakobson, Igor Rivin
We define a number of natural (from geometric and combinatorial points of view) deformation spaces of valuations on finite graphs, and study functions over these deformation spaces…
Growth in free groups (and other stories)
Igor Rivin
We start by studying the distribution of (cyclically reduced) elements of the free groups with respect to their abelianization. We derive an explicit generating function, and a lim…
Simple cycles
Igor Rivin
We obtain sharp bounds for the number of n-cycles in a finite graph as a function of the number of edges, and prove that the complete graph is optimal in more ways than could be im…
On some extremal problems in graph theory
Dmitry Jakobson, Igor Rivin
In this paper we are concerned with various graph invariants (girth, diameter, expansion constants, eigenvalues of the Laplacian, tree number) and their analogs for weighted graphs…