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...
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....
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...
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...
: Hierarchical graphs are graphs with layering structures; clustered graphs are graphs with recursive clustering structures. Both have applications in VLSI design, CASE tools, soft...