[書籍][B] Circuit double cover of graphs

CQ Zhang - 2012 - books.google.com
The famous Circuit Double Cover conjecture (and its numerous variants) is considered one
of the major open problems in graph theory owing to its close relationship with topological …

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 …

A remark on Petersen coloring conjecture of Jaeger

VV Mkrtchyan - ar**. A cycle of is a
connected 2‐regular subgraph. A cycle C is positive if it has an even number of negative …

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 …

[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 …

Five‐cycle double cover and shortest cycle cover

S Liu, RX Hao, R Luo, CQ Zhang - Journal of Graph Theory, 2025 - Wiley Online Library
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 …

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) …