DM
1998
13 years 4 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 4 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 4 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 4 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...
Book
A classic book on graph theory.