One consequence of a long-standing conjecture of Goldberg and Seymour about the chromatic index of multigraphs would be the following statement. Suppose G is a multigraph with maximum degree Δ, such that no vertex subset S of odd size at most Δ induces more than (Δ+1)(|S|-1)/2 edges. Then G has an edge coloring with Δ+1 colors. Here we prove a weakened version of this statement.
- Edge coloring
- Goldberg's conjecture
ASJC Scopus subject areas
- Discrete Mathematics and Combinatorics
- Theoretical Computer Science