Spanning tree (English Wikipedia)

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

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10doi.org

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2arxiv.org

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2web.archive.org

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1networkx.org

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1ucsd.edu

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1youtube.com

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1acm.org

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1ox.ac.uk

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1worldcat.org

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acm.org

dl.acm.org

Gallager, R. G.; Humblet, P. A.; Spira, P. M. (1983), "A distributed algorithm for minimum-weight spanning trees", ACM Transactions on Programming Languages and Systems, 5 (1): 66–77, doi:10.1145/357195.357200, archived from the original on Dec 8, 2023; Gazit, Hillel (1991), "An optimal randomized parallel algorithm for finding connected components in a graph", SIAM Journal on Computing, 20 (6): 1046–1067, doi:10.1137/0220066, MR 1135748; Bader, David A.; Cong, Guojing (2005), "A fast, parallel spanning tree algorithm for symmetric multiprocessors (SMPs)" (PDF), Journal of Parallel and Distributed Computing, 65 (9): 994–1006, doi:10.1016/j.jpdc.2005.03.011, archived from the original (PDF) on Sep 23, 2015.

ams.org

mathscinet.ams.org

Beineke, Lowell W.; Wilson, Robin J. (2009), Topics in topological graph theory, Encyclopedia of Mathematics and its Applications, vol. 128, Cambridge University Press, Cambridge, p. 36, doi:10.1017/CBO9781139087223, ISBN 978-0-521-80230-7, MR 2581536
Harary, Frank; Hayes, John P.; Wu, Horng-Jyh (1988), "A survey of the theory of hypercube graphs", Computers & Mathematics with Applications, 15 (4): 277–289, doi:10.1016/0898-1221(88)90213-1, hdl:2027.42/27522, MR 0949280.
de Fraysseix, Hubert; Rosenstiehl, Pierre (1982), "A depth-first-search characterization of planarity", Graph theory (Cambridge, 1981), Ann. Discrete Math., vol. 13, Amsterdam: North-Holland, pp. 75–80, MR 0671906.
Reif, John H. (1985), "Depth-first search is inherently sequential", Information Processing Letters, 20 (5): 229–234, doi:10.1016/0020-0190(85)90024-9, MR 0801987.
Gallager, R. G.; Humblet, P. A.; Spira, P. M. (1983), "A distributed algorithm for minimum-weight spanning trees", ACM Transactions on Programming Languages and Systems, 5 (1): 66–77, doi:10.1145/357195.357200, archived from the original on Dec 8, 2023; Gazit, Hillel (1991), "An optimal randomized parallel algorithm for finding connected components in a graph", SIAM Journal on Computing, 20 (6): 1046–1067, doi:10.1137/0220066, MR 1135748; Bader, David A.; Cong, Guojing (2005), "A fast, parallel spanning tree algorithm for symmetric multiprocessors (SMPs)" (PDF), Journal of Parallel and Distributed Computing, 65 (9): 994–1006, doi:10.1016/j.jpdc.2005.03.011, archived from the original (PDF) on Sep 23, 2015.
Wilson, David Bruce (1996), "Generating random spanning trees more quickly than the cover time", Proceedings of the Twenty-Eighth Annual ACM Symposium on the Theory of Computing (STOC 1996), pp. 296–303, doi:10.1145/237814.237880, MR 1427525.
McDiarmid, Colin; Johnson, Theodore; Stone, Harold S. (1997), "On finding a minimum spanning tree in a network with random weights" (PDF), Random Structures & Algorithms, 10 (1–2): 187–204, doi:10.1002/(SICI)1098-2418(199701/03)10:1/2<187::AID-RSA10>3.3.CO;2-Y, MR 1611522.
Gabow, Harold N.; Myers, Eugene W. (1978), "Finding all spanning trees of directed and undirected graphs", SIAM Journal on Computing, 7 (3): 280–287, doi:10.1137/0207024, MR 0495152
Soukup, Lajos (2008), "Infinite combinatorics: from finite to infinite", Horizons of combinatorics, Bolyai Soc. Math. Stud., vol. 17, Berlin: Springer, pp. 189–213, doi:10.1007/978-3-540-77200-2_10, MR 2432534. See in particular Theorem 2.1, pp. 192–193.

arxiv.org

Goldberg, L.A.; Jerrum, M. (2008), "Inapproximability of the Tutte polynomial", Information and Computation, 206 (7): 908–929, arXiv:cs/0605140, doi:10.1016/j.ic.2008.04.003; Jaeger, F.; Vertigan, D. L.; Welsh, D. J. A. (1990), "On the computational complexity of the Jones and Tutte polynomials", Mathematical Proceedings of the Cambridge Philosophical Society, 108: 35–53, doi:10.1017/S0305004100068936.
Levine, Lionel (2011). "Sandpile groups and spanning trees of directed line graphs". Journal of Combinatorial Theory, Series A. 118 (2): 350–364. arXiv:0906.2809. doi:10.1016/j.jcta.2010.04.001. ISSN 0097-3165.

books.google.com

Oxley, J. G. (2006), Matroid Theory, Oxford Graduate Texts in Mathematics, vol. 3, Oxford University Press, p. 141, ISBN 978-0-19-920250-8.
Hartsfield, Nora; Ringel, Gerhard (2003), Pearls in Graph Theory: A Comprehensive Introduction, Courier Dover Publications, p. 100, ISBN 978-0-486-43232-8.
Cameron, Peter J. (1994), Combinatorics: Topics, Techniques, Algorithms, Cambridge University Press, p. 163, ISBN 978-0-521-45761-3.
Bollobás, Béla (1998), Modern Graph Theory, Graduate Texts in Mathematics, vol. 184, Springer, p. 350, ISBN 978-0-387-98488-9; Mehlhorn, Kurt (1999), LEDA: A Platform for Combinatorial and Geometric Computing, Cambridge University Press, p. 260, ISBN 978-0-521-56329-1.
Gross, Jonathan L.; Yellen, Jay (2005), Graph Theory and Its Applications (2nd ed.), CRC Press, p. 168, ISBN 978-1-58488-505-4; Bondy, J. A.; Murty, U. S. R. (2008), Graph Theory, Graduate Texts in Mathematics, vol. 244, Springer, p. 578, ISBN 978-1-84628-970-5.
Kocay, William; Kreher, Donald L. (2004), "5.8 The matrix-tree theorem", Graphs, Algorithms, and Optimization, Discrete Mathematics and Its Applications, CRC Press, pp. 111–116, ISBN 978-0-203-48905-5.
Kozen, Dexter (1992), The Design and Analysis of Algorithms, Monographs in Computer Science, Springer, p. 19, ISBN 978-0-387-97687-7.
Soukup, Lajos (2008), "Infinite combinatorics: from finite to infinite", Horizons of combinatorics, Bolyai Soc. Math. Stud., vol. 17, Berlin: Springer, pp. 189–213, doi:10.1007/978-3-540-77200-2_10, MR 2432534. See in particular Theorem 2.1, pp. 192–193.

doi.org

Beineke, Lowell W.; Wilson, Robin J. (2009), Topics in topological graph theory, Encyclopedia of Mathematics and its Applications, vol. 128, Cambridge University Press, Cambridge, p. 36, doi:10.1017/CBO9781139087223, ISBN 978-0-521-80230-7, MR 2581536
Harary, Frank; Hayes, John P.; Wu, Horng-Jyh (1988), "A survey of the theory of hypercube graphs", Computers & Mathematics with Applications, 15 (4): 277–289, doi:10.1016/0898-1221(88)90213-1, hdl:2027.42/27522, MR 0949280.
Goldberg, L.A.; Jerrum, M. (2008), "Inapproximability of the Tutte polynomial", Information and Computation, 206 (7): 908–929, arXiv:cs/0605140, doi:10.1016/j.ic.2008.04.003; Jaeger, F.; Vertigan, D. L.; Welsh, D. J. A. (1990), "On the computational complexity of the Jones and Tutte polynomials", Mathematical Proceedings of the Cambridge Philosophical Society, 108: 35–53, doi:10.1017/S0305004100068936.
Reif, John H. (1985), "Depth-first search is inherently sequential", Information Processing Letters, 20 (5): 229–234, doi:10.1016/0020-0190(85)90024-9, MR 0801987.
Gallager, R. G.; Humblet, P. A.; Spira, P. M. (1983), "A distributed algorithm for minimum-weight spanning trees", ACM Transactions on Programming Languages and Systems, 5 (1): 66–77, doi:10.1145/357195.357200, archived from the original on Dec 8, 2023; Gazit, Hillel (1991), "An optimal randomized parallel algorithm for finding connected components in a graph", SIAM Journal on Computing, 20 (6): 1046–1067, doi:10.1137/0220066, MR 1135748; Bader, David A.; Cong, Guojing (2005), "A fast, parallel spanning tree algorithm for symmetric multiprocessors (SMPs)" (PDF), Journal of Parallel and Distributed Computing, 65 (9): 994–1006, doi:10.1016/j.jpdc.2005.03.011, archived from the original (PDF) on Sep 23, 2015.
Wilson, David Bruce (1996), "Generating random spanning trees more quickly than the cover time", Proceedings of the Twenty-Eighth Annual ACM Symposium on the Theory of Computing (STOC 1996), pp. 296–303, doi:10.1145/237814.237880, MR 1427525.
McDiarmid, Colin; Johnson, Theodore; Stone, Harold S. (1997), "On finding a minimum spanning tree in a network with random weights" (PDF), Random Structures & Algorithms, 10 (1–2): 187–204, doi:10.1002/(SICI)1098-2418(199701/03)10:1/2<187::AID-RSA10>3.3.CO;2-Y, MR 1611522.
Gabow, Harold N.; Myers, Eugene W. (1978), "Finding all spanning trees of directed and undirected graphs", SIAM Journal on Computing, 7 (3): 280–287, doi:10.1137/0207024, MR 0495152
Soukup, Lajos (2008), "Infinite combinatorics: from finite to infinite", Horizons of combinatorics, Bolyai Soc. Math. Stud., vol. 17, Berlin: Springer, pp. 189–213, doi:10.1007/978-3-540-77200-2_10, MR 2432534. See in particular Theorem 2.1, pp. 192–193.
Levine, Lionel (2011). "Sandpile groups and spanning trees of directed line graphs". Journal of Combinatorial Theory, Series A. 118 (2): 350–364. arXiv:0906.2809. doi:10.1016/j.jcta.2010.04.001. ISSN 0097-3165.

gatech.edu

cc.gatech.edu

Gallager, R. G.; Humblet, P. A.; Spira, P. M. (1983), "A distributed algorithm for minimum-weight spanning trees", ACM Transactions on Programming Languages and Systems, 5 (1): 66–77, doi:10.1145/357195.357200, archived from the original on Dec 8, 2023; Gazit, Hillel (1991), "An optimal randomized parallel algorithm for finding connected components in a graph", SIAM Journal on Computing, 20 (6): 1046–1067, doi:10.1137/0220066, MR 1135748; Bader, David A.; Cong, Guojing (2005), "A fast, parallel spanning tree algorithm for symmetric multiprocessors (SMPs)" (PDF), Journal of Parallel and Distributed Computing, 65 (9): 994–1006, doi:10.1016/j.jpdc.2005.03.011, archived from the original (PDF) on Sep 23, 2015.

handle.net

hdl.handle.net

Harary, Frank; Hayes, John P.; Wu, Horng-Jyh (1988), "A survey of the theory of hypercube graphs", Computers & Mathematics with Applications, 15 (4): 277–289, doi:10.1016/0898-1221(88)90213-1, hdl:2027.42/27522, MR 0949280.

networkx.org

"Tree". NetworkX 2.6.2 documentation. Retrieved 2021-12-10. For trees and arborescence, the adjective "spanning" may be added to designate that the graph, when considered as a forest/branching, consists of a single tree/arborescence that includes all nodes in the graph.

ox.ac.uk

stats.ox.ac.uk

McDiarmid, Colin; Johnson, Theodore; Stone, Harold S. (1997), "On finding a minimum spanning tree in a network with random weights" (PDF), Random Structures & Algorithms, 10 (1–2): 187–204, doi:10.1002/(SICI)1098-2418(199701/03)10:1/2<187::AID-RSA10>3.3.CO;2-Y, MR 1611522.

uci.edu

ics.uci.edu

Eppstein, David (1999), "Spanning trees and spanners" (PDF), in Sack, J.-R.; Urrutia, J. (eds.), Handbook of Computational Geometry, Elsevier, pp. 425–461, archived (PDF) from the original on Aug 2, 2023.

ucsd.edu

math.ucsd.edu

Graham, R. L.; Hell, Pavol (1985). "On the History of the Minimum Spanning Tree Problem" (PDF).

web.archive.org

Gallager, R. G.; Humblet, P. A.; Spira, P. M. (1983), "A distributed algorithm for minimum-weight spanning trees", ACM Transactions on Programming Languages and Systems, 5 (1): 66–77, doi:10.1145/357195.357200, archived from the original on Dec 8, 2023; Gazit, Hillel (1991), "An optimal randomized parallel algorithm for finding connected components in a graph", SIAM Journal on Computing, 20 (6): 1046–1067, doi:10.1137/0220066, MR 1135748; Bader, David A.; Cong, Guojing (2005), "A fast, parallel spanning tree algorithm for symmetric multiprocessors (SMPs)" (PDF), Journal of Parallel and Distributed Computing, 65 (9): 994–1006, doi:10.1016/j.jpdc.2005.03.011, archived from the original (PDF) on Sep 23, 2015.
Eppstein, David (1999), "Spanning trees and spanners" (PDF), in Sack, J.-R.; Urrutia, J. (eds.), Handbook of Computational Geometry, Elsevier, pp. 425–461, archived (PDF) from the original on Aug 2, 2023.

worldcat.org

Levine, Lionel (2011). "Sandpile groups and spanning trees of directed line graphs". Journal of Combinatorial Theory, Series A. 118 (2): 350–364. arXiv:0906.2809. doi:10.1016/j.jcta.2010.04.001. ISSN 0097-3165.

youtube.com

Borg, Anita. "Folklore of Network Protocol Design". YouTube. Microsoft Research. Retrieved 13 May 2022.