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COCOON
2007
Springer
13 years 11 months ago
On the Number of Cycles in Planar Graphs
We investigate the maximum number of simple cycles and the maximum number of Hamiltonian cycles in a planar graph G with n vertices. Using the transfer matrix method we construct a...
Kevin Buchin, Christian Knauer, Klaus Kriegel, And...
JCT
2006
134views more  JCT 2006»
13 years 4 months ago
MacLane's planarity criterion for locally finite graphs
MacLane's planarity criterion states that a finite graph is planar if and only if its cycle space has a basis B such that every edge is contained in at most two members of B....
Henning Bruhn, Maya Jakobine Stein
GC
2010
Springer
13 years 3 months ago
20 Years of Negami's Planar Cover Conjecture
In 1988, Seiya Negami published a conjecture stating that a graph G has a finite planar cover (i.e. a homomorphism from some planar graph onto G which maps the vertex neighbourhoo...
Petr Hlinený
STACS
2005
Springer
13 years 10 months ago
Cycle Cover with Short Cycles
Cycle covering is a well-studied problem in computer science. In this paper, we develop approximation algorithms for variants of cycle covering problems which bound the size and/o...
Nicole Immorlica, Mohammad Mahdian, Vahab S. Mirro...
JDA
2010
131views more  JDA 2010»
13 years 3 months ago
Convex drawings of hierarchical planar graphs and clustered planar graphs
: Hierarchical graphs are graphs with layering structures; clustered graphs are graphs with recursive clustering structures. Both have applications in VLSI design, CASE tools, soft...
Seok-Hee Hong, Hiroshi Nagamochi