16,424 research outputs found
Traffic Analysis in Random Delaunay Tessellations and Other Graphs
In this work we study the degree distribution, the maximum vertex and edge
flow in non-uniform random Delaunay triangulations when geodesic routing is
used. We also investigate the vertex and edge flow in Erd\"os-Renyi random
graphs, geometric random graphs, expanders and random -regular graphs.
Moreover we show that adding a random matching to the original graph can
considerably reduced the maximum vertex flow.Comment: Submitted to the Journal of Discrete Computational Geometr
Higher-Order Triangular-Distance Delaunay Graphs: Graph-Theoretical Properties
We consider an extension of the triangular-distance Delaunay graphs
(TD-Delaunay) on a set of points in the plane. In TD-Delaunay, the convex
distance is defined by a fixed-oriented equilateral triangle ,
and there is an edge between two points in if and only if there is an empty
homothet of having the two points on its boundary. We consider
higher-order triangular-distance Delaunay graphs, namely -TD, which contains
an edge between two points if the interior of the homothet of
having the two points on its boundary contains at most points of . We
consider the connectivity, Hamiltonicity and perfect-matching admissibility of
-TD. Finally we consider the problem of blocking the edges of -TD.Comment: 20 page
On the Complexity of the Mis\`ere Version of Three Games Played on Graphs
We investigate the complexity of finding a winning strategy for the mis\`ere
version of three games played on graphs : two variants of the game
, introduced by Stockmann in 2004 and the game on both directed and undirected graphs. We show that on general
graphs those three games are -Hard or Complete. For one
-Hard variant of , we find an algorithm to compute
an effective winning strategy in time when
is a bipartite graph
Disproof of the List Hadwiger Conjecture
The List Hadwiger Conjecture asserts that every -minor-free graph is
-choosable. We disprove this conjecture by constructing a
-minor-free graph that is not -choosable for every integer
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