When can a k‐edge‐coloring of a subgraph K of a graph G be extended to a k‐edge‐coloring of G? One necessary condition is that (Formula Presented.) for all X ⊆ E(G) ‐ E(K), where μi(X) is the maximum cardinality of a subset of X whose union with the set of edges of K colored i is a matching. This condition is not sufficient in general, but is sufficient for graphs of very simple structure. We try to locate the border where sufficiency ends.
All Science Journal Classification (ASJC) codes
- Geometry and Topology