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ALGOSENSORS
2004
Springer
13 years 10 months ago
On a Conjecture Related to Geometric Routing
We conjecture that any planar 3-connected graph can be embedded in the plane in such a way that for any nodes s and t, there is a path from s to t such that the Euclidean distance ...
Christos H. Papadimitriou, David Ratajczak
CORR
2007
Springer
132views Education» more  CORR 2007»
13 years 4 months ago
Nodally 3-connected planar graphs and convex combination mappings
A barycentric mapping of a planar graph is a plane embedding in which every internal vertex is the average of its neighbours. A celebrated result of Tutte’s [16] is that if a pl...
Colm Ó'Dúnlaing
FOCS
2008
IEEE
13 years 11 months ago
Some Results on Greedy Embeddings in Metric Spaces
Geographic Routing is a family of routing algorithms that uses geographic point locations as addresses for the purposes of routing. Such routing algorithms have proven to be both ...
Ankur Moitra, Tom Leighton
EJC
2007
13 years 4 months ago
Chords of longest circuits in locally planar graphs
It was conjectured by Thomassen ([B. Alspach, C. Godsil, Cycle in graphs, Ann. Discrete Math. 27 (1985)], p. 466) that every longest circuit of a 3-connected graph must have a cho...
Ken-ichi Kawarabayashi, Jianbing Niu, Cun-Quan Zha...