359 research outputs found
Rank of divisors on tropical curves
We investigate, using purely combinatorial methods, structural and algorithmic properties of linear equivalence classes of divisors on tropical curves. In particular, we confirm a conjecture of Baker asserting that the rank of a divisor D on a (non-metric) graph is equal to the rank of D on the corresponding metric graph, and construct an algorithm for computing the rank of a divisor on a tropical curve
Loebl-Komlos-Sos Conjecture: dense case
We prove a version of the Loebl-Komlos-Sos Conjecture for dense graphs. For
each q>0 there exists a number such that for any n>n_0 and
k>qn the following holds: if G be a graph of order n with at least n/2 vertices
of degree at least k, then any tree of order k+1 is a subgraph of G.Comment: 56 pages, 8 figures; substantial changes as suggested by a refere
- …