4 papers · 1 filter
Nowhere-zero 8-flows in 3-edge-connected signed graphs
Matt DeVos, Kathryn Nurse, Robert Šámal
In 1983, A. Bouchet extended W.T. Tutte's notion of nowhere-zero flows to signed graphs, and conjectured that every flow-admissible signed graph has a nowhere-zero 6-flow. In this…
On the Ban-Linial Conjecture
Matt DeVos, Kathryn Nurse
Let be a graph and let be a partition of . This partition is called external or unfriendly if every has at least as many neighbours in …
Nowhere-zero 8-flows in cyclically 5-edge-connected, flow-admissible signed graphs
Matt DeVos, Kathryn Nurse, Robert Sámal
In 1983, Bouchet proved that every bidirected graph with a nowhere-zero integer-flow has a nowhere-zero 216-flow, and conjectured that 216 could be replaced with 6. This paper show…
Graphical representations of graphic frame matroids
Rong Chen, Matt DeVos, Daryl Funk +1
A frame matroid M is graphic if there is a graph G with cycle matroid isomorphic to M. In general, if there is one such graph, there will be many. Zaslavsky has shown that frame ma…