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Page 658 of Mathematical Reviews Vol. , Issue 95b
[page]

1995
*
Mathematical Reviews
*

Thomason (4-CAMB; Cambridge)
95b:05122 05C38 05C70
Lai, Hong-Jian (1-WV; Morgantown, WV);
Yu, Xingxing (1-GAIT; Atlanta, GA);
Zhang, Cun Quan (1-WV; Morgantown, WV)

*Small**circuit**double**covers**of**cubic*... The authors prove that if a*cubic**multigraph*G has a cycle*double**cover*, then it has a cycle*double**cover*with at most 2+ |V(G)|/2 cycles. ...##
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Treelike snarks
[article]

2016
*
arXiv
*
pre-print

In addition, we prove that the snarks from this family (we call them treelike snarks) have circular flow number five and admit a 5-cycle

arXiv:1601.00870v1
fatcat:s55n4cqdnrbt5hajdaro5uxrwq
*double**cover*. ... We study snarks whose edges cannot be*covered*by fewer than five perfect matchings. Esperet and Mazzuoccolo found an infinite family*of*such snarks, generalising an example provided by Hagglund. ... If C is a*circuit*in a*cubic*graph G, we let G C denote the*multigraph*obtained by successively contracting each edge*of*C to a vertex. Lemma 7.2 Let G be a*cubic*graph and let C be a*circuit**of*G. ...##
###
Treelike Snarks

2016
*
Electronic Journal of Combinatorics
*

In addition, we prove that the snarks from this family (we call them treelike snarks) have circular flow number $\phi_C (G)\ge5$ and admit a 5-cycle

doi:10.37236/6008
fatcat:zolqjvztd5gz3fpb6mz67xstay
*double**cover*. ... We study snarks whose edges cannot be*covered*by fewer than five perfect matchings. Esperet and Mazzuoccolo found an infinite family*of*such snarks, generalising an example provided by Hägglund. ... If C is a*circuit*in a*cubic*graph G, we let G C denote the*multigraph*obtained by successively contracting each edge*of*C to a vertex. Lemma 11. Let G be a*cubic*graph and let C be a*circuit**of*G. ...##
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Terminal Backup, 3D Matching, and Covering Cubic Graphs

2011
*
SIAM journal on computing (Print)
*

In the process

doi:10.1137/090752699
fatcat:z4jl6yxu3rggxewqhmoyylkusy
*of*this proof we show some powerful new results about*covering**cubic*graphs with simple combinatorial objects. ... Simplex Matching is also useful for various tasks that involve forming groups*of*at least 2 members, such as project assignment and variants*of*facility location. ... Cycle*Double**Cover*Conjecture). ...##
###
Terminal backup, 3D matching, and covering cubic graphs

2007
*
Proceedings of the thirty-ninth annual ACM symposium on Theory of computing - STOC '07
*

In the process

doi:10.1145/1250790.1250849
dblp:conf/stoc/AnshelevichK07
fatcat:h2ou6zfrnbejhmf7twvimn77h4
*of*this proof we show some powerful new results about*covering**cubic*graphs with simple combinatorial objects. ... Simplex Matching is also useful for various tasks that involve forming groups*of*at least 2 members, such as project assignment and variants*of*facility location. ... Cycle*Double**Cover*Conjecture). ...##
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On Survivable Access Network Design: Complexity and Algorithms

2008
*
2008 Proceedings IEEE INFOCOM - The 27th Conference on Computer Communications
*

In the process

doi:10.1109/infocom.2007.46
fatcat:7ylylwhsxfhpvayzgsgudaxoru
*of*this proof we show some powerful new results about*covering**cubic*graphs with simple combinatorial objects. ... Simplex Matching is also useful for various tasks that involve forming groups*of*at least 2 members, such as project assignment and variants*of*facility location. ... Cycle*Double**Cover*Conjecture). ...##
###
On Survivable Access Network Design: Complexity and Algorithms

2008
*
IEEE INFOCOM 2008 - The 27th Conference on Computer Communications
*

*of*this proof we show some powerful new results about

*covering*

*cubic*graphs with simple combinatorial objects. ... Simplex Matching is also useful for various tasks that involve forming groups

*of*at least 2 members, such as project assignment and variants

*of*facility location. ... Cycle

*Double*

*Cover*Conjecture). ...

##
###
How Many Conjectures Can You Stand? A Survey

2011
*
Graphs and Combinatorics
*

These conjectures have lead to a wealth

doi:10.1007/s00373-011-1090-6
fatcat:jj7oxvyx5vhrzdjtv2qyj7nysy
*of*interesting concepts, techniques, results and equivalent conjectures. ... We survey results and open problems in hamiltonian graph theory centered around two conjectures*of*the 1980s that are still open: every 4-connected claw-free graph (line graph) is hamiltonian. ... -Is there a link to conjectures on*Double*Cycle*Covers*? -Is there a link to conjectures on Nowhere-Zero Flows? ...##
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Short Cycle Covers of Graphs with at Most 77% Vertices of Degree Two

2020
*
Electronic Journal of Combinatorics
*

Let $G$ be a bridgeless

doi:10.37236/9284
fatcat:ros4n7grgbddxlc3ynypegfjse
*multigraph*with $m$ edges and $n_2$ vertices*of*degree two and let $cc(G)$ be the length*of*its shortest cycle*cover*. ... It is known that if $cc(G) < 1.4m$ in bridgeless graphs with $n_2 \le m/10$, then the Cycle*Double**Cover*Conjecture holds. ... This conjecture is surprisingly strong as it implies the well-known Cycle*Double**Cover*Conjecture [9] . ...##
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Some snarks are worse than others
[article]

2020
*
arXiv
*
pre-print

The Cycle

arXiv:2004.14049v1
fatcat:npttcm5ju5d75m5cfwxih4elca
*Double**Cover*Conjecture, the Shortest Cycle*Cover*Conjecture and the Fan-Raspaud Conjecture are examples*of*statements for which S_≥ 5 is crucial. ... cannot be*covered*with four perfect matchings. ... G) which can be extendend to a cycle*double**cover**of*G. ...##
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On measures of edge-uncolorability of cubic graphs: A brief survey and some new results
[article]

2017
*
arXiv
*
pre-print

There are many hard conjectures in graph theory, like Tutte's 5-flow conjecture, and the 5-cycle

arXiv:1702.07156v1
fatcat:56e6ysreure75gupsvey2nuu5m
*double**cover*conjecture, which would be true in general if they would be true for*cubic*graphs. ... Since most*of*them are trivially true for 3-edge-colorable*cubic*graphs,*cubic*graphs which are not 3-edge-colorable, often called snarks, play a key role in this context. ... The research*of*the third author on this project was supported by Deutsche Forschungsgemeinschaft (DFG) grant STE 792/2-1. ...##
###
Measures of Edge-Uncolorability of Cubic Graphs

2018
*
Electronic Journal of Combinatorics
*

There are many hard conjectures in graph theory, like Tutte's 5-flow conjecture, and the $5$-cycle

doi:10.37236/6848
fatcat:gp6i46upuzaonfaw3qxfrrg7zm
*double**cover*conjecture, which would be true in general if they would be true for*cubic*graphs. ... Since most*of*them are trivially true for $3$-edge-colorable*cubic*graphs,*cubic*graphs which are not $3$-edge-colorable, often called snarks, play a key role in this context. ... Acknowledgements The authors sincerely acknowledge the useful comments and suggestions*of*the reviewers, which led to a significant improvement*of*this work. ...##
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Efficient algorithms for path partitions

1990
*
Discrete Applied Mathematics
*

An [a, b] path partition is a decomposition

doi:10.1016/0166-218x(90)90070-s
fatcat:zoktqxomyfbxtfoiakhjzqyycy
*of*the edges*of*a graph into a independent path sets and b matchings, where an independent path set is a set*of*paths that do not intersect each other. ... For example, it is known that the edges*of*any*cubic*graph with n vertices can be*covered*by +n edge-disjoint paths [8] . ... Karloff and Shmoys's algorithm for edge-coloring*multigraphs**of*maximum degree 3 also obtains the initial coloring using the technique*of*alternately coloring the edges*of*an Euler*circuit*, but breaks ...##
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Cycle double covers and spanning minors I

2006
*
Journal of combinatorial theory. Series B (Print)
*

We show that every

doi:10.1016/j.jctb.2005.07.004
fatcat:3beinhiiarbtfndjlfxjzg5glm
*cubic*graph with spanning subgraph consisting*of*a subdivision*of*a Kotzig graph together with even cycles has a cycle*double**cover*, in fact a 6-CDC. ... In a sequel we show that every*cubic*graph with a spanning homeomorph*of*a 2-connected*cubic*graph on at most 10 vertices has a CDC. ... Introduction A cycle (or*circuit*)*double**cover**of*a graph G is a collection*of*cycles in G, not necessarily distinct, such that any edge in G belongs to exactly two*of*the cycles. ...##
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Master index of volumes 181–190

1998
*
Discrete Mathematics
*

Kaneta, Classification

doi:10.1016/s0012-365x(98)90328-4
fatcat:s2tsivncvfcilf6jlbl4fx24zq
*of*extremal*double*-circulant self-dual codes*of*length up to 62 188 (1998) Harant, J., A lower bound on the independence number*of*181 Jha, P.K., Kronecker products*of*paths and ... Shyr 181 (1998) Tsukui, Y., Transformations*of*edge-coloured*cubic*graphs 184 (1998) Tuza, Zs., see L. ...
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