In 1966, Tutte presented a problem about matroids which contained as special cases the four-colour problem and two graph-theoretic extensions of it and he gave a conjecture as to the general solution. In this paper we reduce the matroid problem to one of the graph-theoretic special cases (the so-called 4-flow problem), and we show that his general conjecture is correct if it is true in this special case.
All Science Journal Classification (ASJC) codes
- Theoretical Computer Science
- Discrete Mathematics and Combinatorics
- Computational Theory and Mathematics