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Discrete Applied Mathematics, ISSN 0166-218X, 05/2015, Volume 186, Issue 1, pp. 66 - 73
In this paper, a cycle is a graph in which each vertex has even degree. A Fulkerson-cover of a graph G is a set of six cycles such that each edge of G is in... 
Fulkerson-cover | 4-flow | Flip-flop | Hypohamiltonian | Fulkerson conjecture | MATHEMATICS, APPLIED | TUTTE | THEOREMS | FLOWS
Journal Article
Journal of Graph Theory, ISSN 0364-9024, 05/2018, Volume 88, Issue 1, pp. 46 - 60
It is conjectured by Berge and Fulkerson that every bridgeless cubic graph has six perfect matchings such that each edge is contained in exactly two of them.... 
Berge–Fulkerson coloring | perfect matching | oddness | Berge–Fulkerson conjecture | snarks | 4‐flow | 4-flow | MATHEMATICS | CYCLE-DOUBLE COVERS | Berge-Fulkerson conjecture | ODDNESS 4 | CUBIC GRAPHS | Berge-Fulkerson coloring
Journal Article
Graphs and Combinatorics, ISSN 0911-0119, 7/2015, Volume 31, Issue 4, pp. 993 - 1001
Let $$\alpha ^\prime (G)$$ α ′ ( G ) be the maximum number of independent edges in a graph $$G$$ G and $$A$$ A an abelian group with $$|A|\ge 4$$ | A | ≥ 4 .... 
Matching | Mathematics | Engineering Design | Nowhere-zero 4-flow | Combinatorics | Group connectivity | MATHEMATICS | 3-EDGE-CONNECTED GRAPHS | Graphs | Connectivity
Journal Article
Israel Journal of Mathematics, ISSN 0021-2172, 5/2016, Volume 212, Issue 1, pp. 219 - 235
In 1985, Alon and Tarsi conjectured that the length of a shortest cycle cover of a bridgeless graph H is at most 7/5 |E(H|). The conjecture is still open. Let... 
Algebra | Analysis | Theoretical, Mathematical and Computational Physics | Mathematics, general | Mathematics | Group Theory and Generalizations | Applications of Mathematics | MATHEMATICS | NOWHERE-ZERO 4-FLOW | CIRCUIT COVERS | CONJECTURE | Mathematical research | Graph theory | Research
Journal Article
SIAM Journal on Discrete Mathematics, ISSN 0895-4801, 2010, Volume 24, Issue 1, pp. 330 - 355
The shortest cycle cover conjecture of Alon and Tarsi asserts that the edges of every bridgeless graph with m edges can be covered by cycles of total length at... 
Cycle double cover | Shortest cycle cover | Cycle cover | COLORINGS | FULKERSON CONJECTURE | MATHEMATICS, APPLIED | shortest cycle cover | CIRCUIT COVERS | cycle double cover | EULERIAN GRAPHS | cycle cover | NOWHERE-ZERO 4-FLOW | CUBIC GRAPHS | FLOWS | Studies | Graphs
Journal Article
Discrete Mathematics, ISSN 0012-365X, 2009, Volume 309, Issue 5, pp. 1025 - 1032
Tutte [W.T. Tutte, On the algebraic theory of graph colorings, J. Combin. Theory 1 (1966) 15–20] conjectured that every bridgeless Petersen-minor free graph... 
4-flow | Petersen minor | Almost Petersen-minor free graphs | Edge-3-coloring | Integer flow | MATHEMATICS | MATROIDS | EVERY PLANAR MAP
Journal Article
Discrete Mathematics, ISSN 0012-365X, 2002, Volume 259, Issue 1, pp. 337 - 342
Let G be an undirected graph. The Chinese postman problem (CPP) asks for a shortest postman tour in G, i.e., a closed walk using each edge at least once. The... 
4-Flow | Petersen graph | Cycle cover | Faithful cover | Counterexample | 4-flow
Journal Article
Discrete Mathematics, ISSN 0012-365X, 10/2005, Volume 301, Issue 2-3, pp. 232 - 238
Let G be a graph with odd edge-connectivity r. It is proved in this paper that if r>3, then G has a 3-cycle (1,2)-cover of total length at most... 
r-graph | Cycle cover | Shortest cycle cover | Odd-edge connectivity | MATHEMATICS | shortest cycle cover | CIRCUIT COVERS | TUTTE | odd-edge connectivity | INTEGER FLOWS | FULKERSON | cycle cover | NOWHERE-ZERO 4-FLOW | GRAPHS | CONJECTURE
Journal Article
DISCRETE MATHEMATICS, ISSN 0012-365X, 10/2012, Volume 312, Issue 19, pp. 2938 - 2945
Let G = (V, E) be a finite graph and let (A, +) be an abelian group with identity 0. Then G is A-magic if and only if there exists a function phi from E into A... 
MATHEMATICS | Odd factor | Edge-covering | Nowhere-zero 4-flow | A-magic labeling
Journal Article
Journal of Graph Theory, ISSN 0364-9024, 03/1994, Volume 18, Issue 2, pp. 153 - 160
The concept of a (1, 2)‐eulerian weight was introduced and studied in several papers recently by Seymour, Alspach, Goddyn, and Zhang. In this paper, we proved... 
MATHEMATICS | NOWHERE-ZERO 4-FLOW | INTEGER FLOWS | GRAPHS
Journal Article
DISCRETE MATHEMATICS, ISSN 0012-365X, 12/2002, Volume 259, Issue 1-3, pp. 337 - 342
Let G be an undirected graph. The Chinese postman problem (CPP) asks for a shortest postman tour in G, i.e., a closed walk using each edge at least once. The... 
MATHEMATICS | 4-flow | Petersen graph | counterexample | cycle cover | faithful cover | GRAPHS
Journal Article
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