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On the heterochromatic number of hypergraphs associated to geometric graphs and to matroids
hypergraphs associated geometric graphs matroids
2010/11/24
The heterochromatic number hc(H) of a non-empty hypergraph H is the smallest integer k such that for every colouring of the vertices of H with exactly k colours, there is a hyperedge of H all of whos...
Drawing planar graphs of bounded degree with few slopes
planar graphs bounded degree few slopes
2010/12/1
settle a problem of Dujmović, Eppstein, Suderman, and Wood by showing that there exists
a function f with the property that every planar graph G with maximum degree d admits a drawing
with nonc...
We prove an analogue for a one-phase free boundary problem of the classical gradient bound for solutions to the minimal surface equation. It follows, in particular, that every energy-minimizing free b...
Hierarchy Structure of Graphs and Weighted Condensations
Hierarchy Structure Graphs Weighted Condensations
2010/11/1
By natural way the hierarchy structure is introduced on directed graphs with weighted adjacencies. Embedded system of algebras of subsets of the set of vertices of such digraph and it's consolidation...