Flows of 3-edge-colorable cubic signed graphs
نویسندگان
چکیده
Bouchet conjectured in 1983 that every flow-admissible signed graph admits a nowhere-zero 6-flow which is equivalent to the restriction cubic graphs. In this paper, we proved 3-edge-colorable 10-flow. This together with 4-color theorem implies bridgeless planar As byproduct, also show hamiltonian 8-flow.
منابع مشابه
On disjoint matchings in cubic graphs: Maximum 2-edge-colorable and maximum 3-edge-colorable subgraphs
We show that any 2−factor of a cubic graph can be extended to a maximum 3−edge-colorable subgraph. We also show that the sum of sizes of maximum 2− and 3−edge-colorable subgraphs of a cubic graph is at least twice of its number of vertices.
متن کاملTriangle-free Uniquely 3-Edge Colorable Cubic Graphs
This paper presents infinitely many new examples of triangle-free uniquely 3-edge colorable cubic graphs. The only such graph previously known was given by Tutte in 1976.
متن کاملUniquely Edge-3-Colorable Graphs and Snarks
A cubic graph G is uniquely edge-3-colorable if G has precisely one 1-factorization. It is proved in this paper, if a uniquely edge-3-colorable, cubic graph G is cyclically 4-edgeconnected, but not cyclically 5-edge-connected, then G must contain a snark as a minor. This is an approach to a conjecture that every triangle free uniquely edge-3-colorable cubic graph must have the Petersen graph as...
متن کاملNowhere-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...
متن کاملSize of edge-critical uniquely 3-colorable planar graphs
A graph G is uniquely k-colorable if the chromatic number of G is k and G has only one k-coloring up to permutation of the colors. A uniquely k-colorable graph G is edge-critical if G − e is not a uniquely k-colorable graph for any edge e ∈ E(G). Mel’nikov and Steinberg [L. S. Mel’nikov, R. Steinberg, One counterexample for two conjectures on three coloring, Discrete Math. 20 (1977) 203-206] as...
متن کاملذخیره در منابع من
با ذخیره ی این منبع در منابع من، دسترسی به آن را برای استفاده های بعدی آسان تر کنید
ژورنال
عنوان ژورنال: European Journal of Combinatorics
سال: 2023
ISSN: ['1095-9971', '0195-6698']
DOI: https://doi.org/10.1016/j.ejc.2022.103627