DM
1998
13 years 11 months ago
1998
A basis of the cycle space C(G) of a graph G is h-fold if each edge of G occurs in at most h cycles of the basis. The basis number b(G) of G is the least integer h such that C(G) ...
COMBINATORICA
2004
13 years 11 months ago
2004
We extend the basic theory concerning the cycle space of a finite graph to arbitrary infinite graphs, using as infinite cycles the homeomorphic images of the unit circle in the gr...
JCT
2006
13 years 11 months ago
2006
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....
JGT
2008
13 years 11 months ago
2008
: We develop a general model of edge spaces in order to generalize, unify, and simplify previous work on cycle spaces of infinite graphs. We give simple topological criteria to sho...