Nowhere-zero 3-flows in abelian Cayley graphs

Nowhere-zero 3-flows in Cayley Graphs of Abelian Groups

Nowhere-zero 3-flows in abelian Cayley graphs

We characterize Cayley graphs of abelian groupswhich admit a nowhere-zero 3-flow. In particular, we prove that every k-valent Cayley graph of an abelian group, where k 4, admits a nowhere-zero

Nowhere-Zero 3-Flows in Signed Graphs

Tutte observed that every nowhere-zero k-flow on a plane graph gives rise to a kvertex-coloring of its dual, and vice versa. Thus nowhere-zero integer flow and graph coloring can be viewed as dual concepts. Jaeger further shows that if a graph G has a face-k-colorable 2-cell embedding in some orientable surface, then it has a nowhere-zero k-flow. However, if the surface is nonorientable, then a...

Title Nowhere - Zero 3 - Flows in Signed Graphs

Tutte observed that every nowhere-zero k-flow on a plane graph gives rise to a kvertex-coloring of its dual, and vice versa. Thus nowhere-zero integer flow and graph coloring can be viewed as dual concepts. Jaeger further shows that if a graph G has a face-k-colorable 2-cell embedding in some orientable surface, then it has a nowhere-zero k-flow. However, if the surface is nonorientable, then a...

Nowhere-Zero 3-Flows in Squares of Graphs

It was conjectured by Tutte that every 4-edge-connected graph admits a nowherezero 3-flow. In this paper, we give a complete characterization of graphs whose squares admit nowhere-zero 3-flows and thus confirm Tutte’s 3-flow conjecture for the family of squares of graphs.