Nowhere-zero ows in random graphs

Nowhere-zero 3- ows in squares of graphs

Nowhere-Zero Flows in Random Graphs

A nowhere-zero 3-flow in a graph G is an assignment of a direction and a value of 1 or 2 to each edge of G such that, for each vertex v in G, the sum of the values of the edges with tail v equals the sum of the values of the edges with head v. Motivated by results about the region coloring of planar graphs, Tutte conjectured in 1966 that every 4-edge-connected graph has a nowhere-zero 3-flow. T...

Tutte's 5-flow conjecture for graphs of nonorientable genus 5

We develop four constructions for nowhere-zero 5-ows of 3-regular graphs which satisfy special structural conditions. Using these constructions we show a minimal counterexample to Tutte's 5-ow conjecture is of order 44 and therefore every bridgeless graph of nonorientable genus 5 has a nowhere-zero 5-ow. One of the structural properties is formulated in terms of the structure of the multigraph ...

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 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...