# Nowhere-Zero 5-Flows and Even (1,2)-Factors

M. Matamala, J. Zamora

1 Cita (Scopus)

### Resumen

A graph G = (V, E) admits a nowhere-zero k-flow if there exists an orientation H = (V, A) of G and an integer flow φ: A → ℤ such that for all a ∈ A, 0 < {pipe}φ(a){pipe} < K. Tutte conjectured that every bridgeless graphs admits a nowhere-zero 5-flow. A (1,2)-factor of G is a set F ⊆ E such that the degree of any vertex v in the subgraph induced by F is 1 or 2. Let us call an edge of G, F-balanced if either it belongs to F or both its ends have the same degree in F. Call a cycle of GF-even if it has an even number of F-balanced edges. A (1,2)-factor F of G is even if each cycle of G is F-even. The main result of the paper is that a cubic graph G admits a nowhere-zero 5-flow if and only if G has an even (1,2)-factor.

Idioma original English 609-616 8 Graphs and Combinatorics 29 3 https://doi.org/10.1007/s00373-011-1119-x Published - may 2013

### Huella dactilar

Nowhere-zero Flow
Pipe
Cycle
Even number
Cubic Graph
Induced Subgraph
Graph in graph theory
If and only if
Integer
Zero
Vertex of a graph

### ASJC Scopus subject areas

• Discrete Mathematics and Combinatorics
• Theoretical Computer Science

### Citar esto

Matamala, M. ; Zamora, J. / Nowhere-Zero 5-Flows and Even (1,2)-Factors. En: Graphs and Combinatorics. 2013 ; Vol. 29, N.º 3. pp. 609-616.
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Nowhere-Zero 5-Flows and Even (1,2)-Factors. / Matamala, M.; Zamora, J.

En: Graphs and Combinatorics, Vol. 29, N.º 3, 05.2013, p. 609-616.

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AU - Zamora, J.

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