Woodall's conjecture: Bibliography

A. Abdi, G. Cornuéjols, M. Zlatin, On packing dijoins in digraphs and weighted digraphs, SIAM Journal on Discrete Mathematics, 37, 2417-2461, 2023.

Jochen Pascal Gollin, Karl Heuer, Konstantinos Stavropoulos, Disjoint dijoins for classes of dicuts in finite and infinite digraphs, Combinatorial Theory, 2022.

Maria Chudnovsky, Katherine Edwards, Ringi Kim, Alex Scott, Paul Seymour.  Disjoint dijoins, Journal of Combinatorial Theory, Series B, v.120, 2016.

F. B. Shepherd and A. Vetta.  Visualizing, finding and packing dijoins.  In D. Avis, A. Hertz, and O. Marcotte, editors, Graph Theory and Combinatorial Optimization. Chapter 8, pp.219–254. Springer Verlag, 2005.

A. M. Williams and B. Guenin.  Advances in packing directed joins. Electronic Notes in Discrete Mathematics, vol.19, pp.249–255, 2005. [Proceedings of the 2nd Brazilian Symposium on Graphs, Algorithms, and Combinatorics (GRACO2005)].

A. M. Williams.  Packing directed joins.  Master's thesis, University of Waterloo, 2004.

A. Schrijver.  Combinatorial Optimization: Polyhedra and Efficiency.  Number 24 in Algorithms and Combinatorics. Springer, 2003.

G. Cornuéjols and B. Guenin.  Note on dijoinsDiscrete Mathematics, vol.243, pp.213–216, 2002.

A. Schrijver.  Min-max relations for directed graphs, Annals of Discrete Mathematics vol.16, pp.261–280, North-Holland, 1982.

A. Schrijver.  A counterexample to a conjecture of Edmonds and GilesDiscrete Mathematics, vol.32, pp.213–214, 1980.

J. Edmonds and R. Giles.  A min-max relation for submodular functions on graphsAnnals of Discrete Mathematics, v.1, pp.185–204. North-Holland, 1977.

D. R. WoodallMenger and König systemsLecture Notes in Mathematics, vol.642, pp.620–635. Springer, 1978.

D. R. WoodallMinimax theorems in graph theorySelected Topics in Graph Theory, pp.237–269. Academic Press, 1978.

C. L. Lucchesi and D. H. Younger.  A minimax theorem for directed graphsJ. of the London Math. Soc. (2), vol.17, pp.369–374, 1978.

Special cases

Y. Wakabayashi and O. Lee.  A note on a min-max conjecture of WoodallJ. Graph Theory. vol.38, pp.36–41, 2001.

P. Feofiloff and D. H. Younger.  Directed cut transversal packing for source-sink connected graphsCombinatorica, vol.7, pp.255–263, 1987.

L. Lovász,  On two minimax theorems in graph theory, J. of Combinatorial Theory (B), vol.21, 1976, pp.96--103.

D.R. Fulkerson, G.C. Harding,  On edge-disjoint branchings, Networks vol.6, 1976, pp.97-104.

R. E. Tarjan,  A good algorithm for edge-disjoint branchingsInformation Processing Letters, vol.3, 1974, pp.51–53.

J. Edmonds.  Edge-disjoint branchings.  In R. Rustin, editor, Combinatorial Algorithms, volume 9 of Courant Computer Science Symposium, pp.91–96. Algorithmics Press, 1973.

WWW sites

Problem 12 in the collection of problems of the Egerváry Research Group on Combinatorial Optimization (EGRES)

Woodall's conjecture, Egerváry Research Group on Combinatorial Optimization (EGRES)

Woodall's Conjecture in Open Problemas Garden, hosted by CSI of Charles University

Cuts in Digraphs and Woodall's Conjecture, in Problems in Topological Graph Theory, compiled by Dan Archdeacon

Clutters

G. Cornuéjols.  Combinatorial Optimization: Packing and Covering.  Volume 74 of CBMS-NSF Regional Conference Series in Applied Mathematics. SIAM (Society for Industrial and Applied Mathematics), 2001.

G. Cornuéjols, B. Guenin, and F. Margot.  The packing propertyMathematical Programming (Ser. A), vol.89, pp.113–126, 2000.

P. D. Seymour.  The matroids with max-flow min-cut propertyJ. of Combinatorial Theory (Ser. B), vol.23, pp.189–222, 1977.