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» On the Number of Cycles in Planar Graphs
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ALGORITHMICA
1998
94views more  ALGORITHMICA 1998»
13 years 7 months ago
A Fully Dynamic Approximation Scheme for Shortest Paths in Planar Graphs
In this paper we give a fully dynamic approximation scheme for maintaining all-pairs shortest paths in planar networks. Given an error parameter ε such that 0 < ε, our algorit...
Philip N. Klein, Sairam Subramanian
COCOON
1999
Springer
14 years 3 days ago
An External Memory Data Structure for Shortest Path Queries
We present results related to satisfying shortest path queries on a planar graph stored in external memory. Let N denote the number of vertices in the graph and let sort(N) denote...
David A. Hutchinson, Anil Maheshwari, Norbert Zeh
BIRTHDAY
2009
Springer
14 years 2 months ago
Properly Coloured Cycles and Paths: Results and Open Problems
In this paper, we consider a number of results and six conjectures on properly coloured (PC) paths and cycles in edge-coloured multigraphs. We overview some known results and prov...
Gregory Gutin, Eun Jung Kim
JGT
2007
54views more  JGT 2007»
13 years 7 months ago
Overlap in consistent cycles
: A (directed) cycle C in a graph is called consistent provided there exists an automorphism of , acting as a 1-step rotation of C. A beautiful but not well-known result of J.H. Co...
Stefko Miklavic, Primoz Potocnik, Steve Wilson
DAM
2008
83views more  DAM 2008»
13 years 7 months ago
Spanning forests and the golden ratio
For a graph G, let fij be the number of spanning rooted forests in which vertex j belongs to a tree rooted at i. In this paper, we show that for a path, the fij's can be expr...
Pavel Chebotarev