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On cubic bridgeless graphs whose edge‐set cannot be covered by four perfect matchings
L Esperet, G Mazzuoccolo - Journal of Graph Theory, 2014 - Wiley Online Library
The problem of establishing the number of perfect matchings necessary to cover the edge‐
set of a cubic bridgeless graph is strictly related to a famous conjecture of Berge and …
set of a cubic bridgeless graph is strictly related to a famous conjecture of Berge and …
On Fan's conjecture about 4-flow
D Song, S Li, X Wang - Graphs and Combinatorics, 2025 - Springer
To research the shorter circuit cover in a bridgeless graph, Fan conjectured that if G/C
admits a nowhere-zero 4-flow, then G admits a 4-flow f such that E (G)-E (C)⊆ supp (f) and …
admits a nowhere-zero 4-flow, then G admits a 4-flow f such that E (G)-E (C)⊆ supp (f) and …
[HTML][HTML] Short signed circuit covers of signed graphs
J Chen, G Fan - Discrete Applied Mathematics, 2018 - Elsevier
A signed graph G is a graph associated with a map** σ: E (G)→{+ 1,− 1}. An edge e∈ E
(G) is positive if σ (e)= 1 and negative if σ (e)=− 1. A circuit in G is balanced if it contains an …
(G) is positive if σ (e)= 1 and negative if σ (e)=− 1. A circuit in G is balanced if it contains an …
Five‐cycle double cover and shortest cycle cover
The 5‐even subgraph cycle double cover conjecture (5‐CDC conjecture) asserts that every
bridgeless graph has a 5‐even subgraph double cover. A shortest even subgraph cover of a …
bridgeless graph has a 5‐even subgraph double cover. A shortest even subgraph cover of a …
Note on Integer 4-flows in Graphs
X Wang, Y Lu, SG Zhang - Acta Mathematica Sinica, English Series, 2022 - Springer
Let G be a bridgeless graph and C be a circuit in G. To find a shorter circuit cover of G, Fan
proposed a conjecture that if G/C admits a nowhere-zero 4-flow, then G admits a 4-flow (D, f) …
proposed a conjecture that if G/C admits a nowhere-zero 4-flow, then G admits a 4-flow (D, f) …