Pseudoforest (English Wikipedia)

Analysis of information sources in references of the Wikipedia article "Pseudoforest" in English language version.

refsWebsite

Global rank English rank

15doi.org

2^nd place

8semanticscholar.org

11^th place

8^th place

2harvard.edu

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2ams.org

451^st place

277^th place

1handle.net

102^nd place

76^th place

1arxiv.org

69^th place

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1oeis.org

742^nd place

538^th place

1web.archive.org

1^st place

1psu.edu

207^th place

136^th place

1stephenwolfram.com

low place

1jstor.org

26^th place

20^th place

1binghamton.edu

low place

9,533^rd place

1graphclasses.org

low place

1episciences.org

low place

1purdue.edu

850^th place

625^th place

ams.org

mathscinet.ams.org

White (1913); Colbourn, Colbourn & Rosenbaum (1982); Stinson (1983). White, H. S. (1913), "Triple-systems as transformations, and their paths among triads", Transactions of the American Mathematical Society, 14 (1), American Mathematical Society: 6–13, doi:10.2307/1988765, JSTOR 1988765. Colbourn, Marlene J.; Colbourn, Charles J.; Rosenbaum, Wilf L. (1982), "Trains: an invariant for Steiner triple systems", Ars Combinatoria, 13: 149–162, MR 0666934. Stinson, D. R. (1983), "A comparison of two invariants for Steiner triple systems: fragments and trains", Ars Combinatoria, 16: 69–76, MR 0734047.
Matthews (1977). Matthews, L. R. (1977), "Bicircular matroids", The Quarterly Journal of Mathematics, Second Series, 28 (110): 213–227, doi:10.1093/qmath/28.2.213, MR 0505702.

arxiv.org

Streinu & Theran (2009). Streinu, I.; Theran, L. (2009), "Sparsity-certifying Graph Decompositions", Graphs and Combinatorics, 25 (2): 219, arXiv:0704.0002, doi:10.1007/s00373-008-0834-4, S2CID 15877017.

binghamton.edu

math.binghamton.edu

Glossary of Signed and Gain Graphs and Allied Areas

doi.org

Gabow & Tarjan (1988). Gabow, H. N.; Tarjan, R. E. (1988), "A linear-time algorithm for finding a minimum spanning pseudoforest", Information Processing Letters, 27 (5): 259–263, doi:10.1016/0020-0190(88)90089-0.
This is the definition used, e.g., by Gabow & Westermann (1992). Gabow, H. N.; Westermann, H. H. (1992), "Forests, frames, and games: Algorithms for matroid sums and applications", Algorithmica, 7 (1): 465–497, doi:10.1007/BF01758774, S2CID 40358357.
This is the definition in Gabow & Tarjan (1988). Gabow, H. N.; Tarjan, R. E. (1988), "A linear-time algorithm for finding a minimum spanning pseudoforest", Information Processing Letters, 27 (5): 259–263, doi:10.1016/0020-0190(88)90089-0.
See, e.g., the proof of Lemma 4 in Àlvarez, Blesa & Serna (2002). Àlvarez, Carme; Blesa, Maria; Serna, Maria (2002), "Universal stability of undirected graphs in the adversarial queueing model", Proc. 14th ACM Symposium on Parallel Algorithms and Architectures, pp. 183–197, doi:10.1145/564870.564903, hdl:2117/97553, ISBN 1-58113-529-7, S2CID 14384161.
Kruskal, Rudolph & Snir (1990) instead use the opposite definition, in which each vertex has indegree one; the resulting graphs, which they call unicycular, are the transposes of the graphs considered here. Kruskal, Clyde P.; Rudolph, Larry; Snir, Marc (1990), "Efficient parallel algorithms for graph problems", Algorithmica, 5 (1): 43–64, doi:10.1007/BF01840376, S2CID 753980.
Woodall (1969); Lovász, Pach & Szegedy (1997). Woodall, D. R. (1969), "Thrackles and deadlock", in Welsh, D. J. A. (ed.), Combinatorial Mathematics and Its Applications, Academic Press, pp. 335–348. Lovász, L.; Pach, J.; Szegedy, M. (1997), "On Conway's thrackle conjecture", Discrete and Computational Geometry, 18 (4): 369–376, doi:10.1007/PL00009322.
Streinu & Theran (2009). Streinu, I.; Theran, L. (2009), "Sparsity-certifying Graph Decompositions", Graphs and Combinatorics, 25 (2): 219, arXiv:0704.0002, doi:10.1007/s00373-008-0834-4, S2CID 15877017.
Whiteley (1988). Whiteley, W. (1988), "The union of matroids and the rigidity of frameworks", SIAM Journal on Discrete Mathematics, 1 (2): 237–255, doi:10.1137/0401025.
Martin, Odlyzko & Wolfram (1984). Martin, O.; Odlyzko, A. M.; Wolfram, S. (1984), "Algebraic properties of cellular automata", Communications in Mathematical Physics, 93 (2): 219–258, Bibcode:1984CMaPh..93..219M, CiteSeerX 10.1.1.78.212, doi:10.1007/BF01223745, S2CID 6900060, archived from the original on 2012-02-12, retrieved 2007-10-03.
White (1913); Colbourn, Colbourn & Rosenbaum (1982); Stinson (1983). White, H. S. (1913), "Triple-systems as transformations, and their paths among triads", Transactions of the American Mathematical Society, 14 (1), American Mathematical Society: 6–13, doi:10.2307/1988765, JSTOR 1988765. Colbourn, Marlene J.; Colbourn, Charles J.; Rosenbaum, Wilf L. (1982), "Trains: an invariant for Steiner triple systems", Ars Combinatoria, 13: 149–162, MR 0666934. Stinson, D. R. (1983), "A comparison of two invariants for Steiner triple systems: fragments and trains", Ars Combinatoria, 16: 69–76, MR 0734047.
Simoes-Pereira (1972). Simoes-Pereira, J. M. S. (1972), "On subgraphs as matroid cells", Mathematische Zeitschrift, 127 (4): 315–322, doi:10.1007/BF01111390, S2CID 186231673.
Matthews (1977). Matthews, L. R. (1977), "Bicircular matroids", The Quarterly Journal of Mathematics, Second Series, 28 (110): 213–227, doi:10.1093/qmath/28.2.213, MR 0505702.
El-Mallah & Colbourn (1988). El-Mallah, Ehab; Colbourn, Charles J. (1988), "The complexity of some edge deletion problems", IEEE Transactions on Circuits and Systems, 35 (3): 354–362, doi:10.1109/31.1748.
Gabow & Westermann (1992). See also the faster approximation schemes of Kowalik (2006). Gabow, H. N.; Westermann, H. H. (1992), "Forests, frames, and games: Algorithms for matroid sums and applications", Algorithmica, 7 (1): 465–497, doi:10.1007/BF01758774, S2CID 40358357. Kowalik, Ł. (2006), "Approximation Scheme for Lowest Outdegree Orientation and Graph Density Measures", in Asano, Tetsuo (ed.), Proceedings of the International Symposium on Algorithms and Computation, Lecture Notes in Computer Science, vol. 4288, Springer-Verlag, pp. 557–566, doi:10.1007/11940128, ISBN 978-3-540-49694-6.
Goldberg, Plotkin & Shannon (1988); Kruskal, Rudolph & Snir (1990). Goldberg, A. V.; Plotkin, S. A.; Shannon, G. E. (1988), "Parallel symmetry-breaking in sparse graphs", SIAM Journal on Discrete Mathematics, 1 (4): 434–446, doi:10.1137/0401044. Kruskal, Clyde P.; Rudolph, Larry; Snir, Marc (1990), "Efficient parallel algorithms for graph problems", Algorithmica, 5 (1): 43–64, doi:10.1007/BF01840376, S2CID 753980.

episciences.org

dmtcs.episciences.org

Kutzelnigg (2006). Kutzelnigg, Reinhard (2006), "Bipartite random graphs and cuckoo hashing", Fourth Colloquium on Mathematics and Computer Science, Discrete Mathematics and Theoretical Computer Science, vol. AG, pp. 403–406.

graphclasses.org

For this terminology, see the list of small graphs from the Information System on Graph Class Inclusions. However, butterfly graph may also refer to a different family of graphs related to hypercubes, and the five-vertex figure 8 is sometimes instead called a bowtie graph.

handle.net

hdl.handle.net

See, e.g., the proof of Lemma 4 in Àlvarez, Blesa & Serna (2002). Àlvarez, Carme; Blesa, Maria; Serna, Maria (2002), "Universal stability of undirected graphs in the adversarial queueing model", Proc. 14th ACM Symposium on Parallel Algorithms and Architectures, pp. 183–197, doi:10.1145/564870.564903, hdl:2117/97553, ISBN 1-58113-529-7, S2CID 14384161.

harvard.edu

ui.adsabs.harvard.edu

Riddell (1951); see OEIS: A057500 in the On-Line Encyclopedia of Integer Sequences. Riddell, R. J. (1951), Contributions to the Theory of Condensation, Ph.D. thesis, Ann Arbor: University of Michigan, Bibcode:1951PhDT........20R.
Martin, Odlyzko & Wolfram (1984). Martin, O.; Odlyzko, A. M.; Wolfram, S. (1984), "Algebraic properties of cellular automata", Communications in Mathematical Physics, 93 (2): 219–258, Bibcode:1984CMaPh..93..219M, CiteSeerX 10.1.1.78.212, doi:10.1007/BF01223745, S2CID 6900060, archived from the original on 2012-02-12, retrieved 2007-10-03.

jstor.org

White (1913); Colbourn, Colbourn & Rosenbaum (1982); Stinson (1983). White, H. S. (1913), "Triple-systems as transformations, and their paths among triads", Transactions of the American Mathematical Society, 14 (1), American Mathematical Society: 6–13, doi:10.2307/1988765, JSTOR 1988765. Colbourn, Marlene J.; Colbourn, Charles J.; Rosenbaum, Wilf L. (1982), "Trains: an invariant for Steiner triple systems", Ars Combinatoria, 13: 149–162, MR 0666934. Stinson, D. R. (1983), "A comparison of two invariants for Steiner triple systems: fragments and trains", Ars Combinatoria, 16: 69–76, MR 0734047.

oeis.org

Riddell (1951); see OEIS: A057500 in the On-Line Encyclopedia of Integer Sequences. Riddell, R. J. (1951), Contributions to the Theory of Condensation, Ph.D. thesis, Ann Arbor: University of Michigan, Bibcode:1951PhDT........20R.

psu.edu

citeseerx.ist.psu.edu

Martin, Odlyzko & Wolfram (1984). Martin, O.; Odlyzko, A. M.; Wolfram, S. (1984), "Algebraic properties of cellular automata", Communications in Mathematical Physics, 93 (2): 219–258, Bibcode:1984CMaPh..93..219M, CiteSeerX 10.1.1.78.212, doi:10.1007/BF01223745, S2CID 6900060, archived from the original on 2012-02-12, retrieved 2007-10-03.

purdue.edu

docs.lib.purdue.edu

Goldberg, Plotkin & Shannon (1988); Kruskal, Rudolph & Snir (1990). Goldberg, A. V.; Plotkin, S. A.; Shannon, G. E. (1988), "Parallel symmetry-breaking in sparse graphs", SIAM Journal on Discrete Mathematics, 1 (4): 434–446, doi:10.1137/0401044. Kruskal, Clyde P.; Rudolph, Larry; Snir, Marc (1990), "Efficient parallel algorithms for graph problems", Algorithmica, 5 (1): 43–64, doi:10.1007/BF01840376, S2CID 753980.

semanticscholar.org

api.semanticscholar.org

This is the definition used, e.g., by Gabow & Westermann (1992). Gabow, H. N.; Westermann, H. H. (1992), "Forests, frames, and games: Algorithms for matroid sums and applications", Algorithmica, 7 (1): 465–497, doi:10.1007/BF01758774, S2CID 40358357.
See, e.g., the proof of Lemma 4 in Àlvarez, Blesa & Serna (2002). Àlvarez, Carme; Blesa, Maria; Serna, Maria (2002), "Universal stability of undirected graphs in the adversarial queueing model", Proc. 14th ACM Symposium on Parallel Algorithms and Architectures, pp. 183–197, doi:10.1145/564870.564903, hdl:2117/97553, ISBN 1-58113-529-7, S2CID 14384161.
Kruskal, Rudolph & Snir (1990) instead use the opposite definition, in which each vertex has indegree one; the resulting graphs, which they call unicycular, are the transposes of the graphs considered here. Kruskal, Clyde P.; Rudolph, Larry; Snir, Marc (1990), "Efficient parallel algorithms for graph problems", Algorithmica, 5 (1): 43–64, doi:10.1007/BF01840376, S2CID 753980.
Streinu & Theran (2009). Streinu, I.; Theran, L. (2009), "Sparsity-certifying Graph Decompositions", Graphs and Combinatorics, 25 (2): 219, arXiv:0704.0002, doi:10.1007/s00373-008-0834-4, S2CID 15877017.
Martin, Odlyzko & Wolfram (1984). Martin, O.; Odlyzko, A. M.; Wolfram, S. (1984), "Algebraic properties of cellular automata", Communications in Mathematical Physics, 93 (2): 219–258, Bibcode:1984CMaPh..93..219M, CiteSeerX 10.1.1.78.212, doi:10.1007/BF01223745, S2CID 6900060, archived from the original on 2012-02-12, retrieved 2007-10-03.
Simoes-Pereira (1972). Simoes-Pereira, J. M. S. (1972), "On subgraphs as matroid cells", Mathematische Zeitschrift, 127 (4): 315–322, doi:10.1007/BF01111390, S2CID 186231673.
Gabow & Westermann (1992). See also the faster approximation schemes of Kowalik (2006). Gabow, H. N.; Westermann, H. H. (1992), "Forests, frames, and games: Algorithms for matroid sums and applications", Algorithmica, 7 (1): 465–497, doi:10.1007/BF01758774, S2CID 40358357. Kowalik, Ł. (2006), "Approximation Scheme for Lowest Outdegree Orientation and Graph Density Measures", in Asano, Tetsuo (ed.), Proceedings of the International Symposium on Algorithms and Computation, Lecture Notes in Computer Science, vol. 4288, Springer-Verlag, pp. 557–566, doi:10.1007/11940128, ISBN 978-3-540-49694-6.
Goldberg, Plotkin & Shannon (1988); Kruskal, Rudolph & Snir (1990). Goldberg, A. V.; Plotkin, S. A.; Shannon, G. E. (1988), "Parallel symmetry-breaking in sparse graphs", SIAM Journal on Discrete Mathematics, 1 (4): 434–446, doi:10.1137/0401044. Kruskal, Clyde P.; Rudolph, Larry; Snir, Marc (1990), "Efficient parallel algorithms for graph problems", Algorithmica, 5 (1): 43–64, doi:10.1007/BF01840376, S2CID 753980.

stephenwolfram.com

Martin, Odlyzko & Wolfram (1984). Martin, O.; Odlyzko, A. M.; Wolfram, S. (1984), "Algebraic properties of cellular automata", Communications in Mathematical Physics, 93 (2): 219–258, Bibcode:1984CMaPh..93..219M, CiteSeerX 10.1.1.78.212, doi:10.1007/BF01223745, S2CID 6900060, archived from the original on 2012-02-12, retrieved 2007-10-03.

web.archive.org

Martin, Odlyzko & Wolfram (1984). Martin, O.; Odlyzko, A. M.; Wolfram, S. (1984), "Algebraic properties of cellular automata", Communications in Mathematical Physics, 93 (2): 219–258, Bibcode:1984CMaPh..93..219M, CiteSeerX 10.1.1.78.212, doi:10.1007/BF01223745, S2CID 6900060, archived from the original on 2012-02-12, retrieved 2007-10-03.