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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.  ... 

Treelike snarks [article]

Marién Abreu, Tomas Kaiser, Domenico Labbate, Giuseppe Mazzuoccolo
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 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.  ... 
arXiv:1601.00870v1 fatcat:s55n4cqdnrbt5hajdaro5uxrwq

Treelike Snarks

Marién Abreu, Tomáš Kaiser, Domenico Labbate, Giuseppe Mazzuoccolo
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 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.  ... 
doi:10.37236/6008 fatcat:zolqjvztd5gz3fpb6mz67xstay

Terminal Backup, 3D Matching, and Covering Cubic Graphs

Elliot Anshelevich, Adriana Karagiozova
2011 SIAM journal on computing (Print)  
In the process 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).  ... 
doi:10.1137/090752699 fatcat:z4jl6yxu3rggxewqhmoyylkusy

Terminal backup, 3D matching, and covering cubic graphs

Elliot Anshelevich, Adriana Karagiozova
2007 Proceedings of the thirty-ninth annual ACM symposium on Theory of computing - STOC '07  
In the process 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).  ... 
doi:10.1145/1250790.1250849 dblp:conf/stoc/AnshelevichK07 fatcat:h2ou6zfrnbejhmf7twvimn77h4

On Survivable Access Network Design: Complexity and Algorithms

D. Xu, E. Anshelevich, M. Chiang
2008 2008 Proceedings IEEE INFOCOM - The 27th Conference on Computer Communications  
In the process 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).  ... 
doi:10.1109/infocom.2007.46 fatcat:7ylylwhsxfhpvayzgsgudaxoru

On Survivable Access Network Design: Complexity and Algorithms

D. Xu, E. Anshelevich, M. Chiang
2008 IEEE INFOCOM 2008 - The 27th Conference on Computer Communications  
In the process 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).  ... 
doi:10.1109/infocom.2008.46 dblp:conf/infocom/XuAC08 fatcat:rv6i52ll2fa3zabkl7nzajadkq

How Many Conjectures Can You Stand? A Survey

H. J. Broersma, Z. Ryjáček, P. Vrána
2011 Graphs and Combinatorics  
These conjectures have lead to a wealth 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?  ... 
doi:10.1007/s00373-011-1090-6 fatcat:jj7oxvyx5vhrzdjtv2qyj7nysy

Short Cycle Covers of Graphs with at Most 77% Vertices of Degree Two

Anna Kompišová, Robert Lukot'ka
2020 Electronic Journal of Combinatorics  
Let $G$ be a bridgeless 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] .  ... 
doi:10.37236/9284 fatcat:ros4n7grgbddxlc3ynypegfjse

Some snarks are worse than others [article]

Edita Máčajová, Giuseppe Mazzuoccolo, Vahan Mkrtchyan, Jean Paul Zerafa
2020 arXiv   pre-print
The Cycle 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.  ... 
arXiv:2004.14049v1 fatcat:npttcm5ju5d75m5cfwxih4elca

On measures of edge-uncolorability of cubic graphs: A brief survey and some new results [article]

M.A. Fiol, G. Mazzuoccolo, E. Steffen
2017 arXiv   pre-print
There are many hard conjectures in graph theory, like Tutte's 5-flow conjecture, and the 5-cycle 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.  ... 
arXiv:1702.07156v1 fatcat:56e6ysreure75gupsvey2nuu5m

Measures of Edge-Uncolorability of Cubic Graphs

M. A. Fiol, G. Mazzuoccolo, E. Steffen
2018 Electronic Journal of Combinatorics  
There are many hard conjectures in graph theory, like Tutte's 5-flow conjecture, and the $5$-cycle 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.  ... 
doi:10.37236/6848 fatcat:gp6i46upuzaonfaw3qxfrrg7zm

Efficient algorithms for path partitions

Craig Williams, Dana Richards
1990 Discrete Applied Mathematics  
An [a, b] path partition is a decomposition 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  ... 
doi:10.1016/0166-218x(90)90070-s fatcat:zoktqxomyfbxtfoiakhjzqyycy

Cycle double covers and spanning minors I

Roland Häggkvist, Klas Markström
2006 Journal of combinatorial theory. Series B (Print)  
We show that every 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.  ... 
doi:10.1016/j.jctb.2005.07.004 fatcat:3beinhiiarbtfndjlfxjzg5glm

Master index of volumes 181–190

1998 Discrete Mathematics  
Kaneta, Classification 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.  ... 
doi:10.1016/s0012-365x(98)90328-4 fatcat:s2tsivncvfcilf6jlbl4fx24zq
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