Three utilities problem (English Wikipedia)

Analysis of information sources in references of the Wikipedia article "Three utilities problem" in English language version.

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13doi.org

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11ams.org

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6semanticscholar.org

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4archive.org

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3harvard.edu

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1uni-goettingen.de

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ams.org

mathscinet.ams.org

Beineke, Lowell; Wilson, Robin (2010), "The early history of the brick factory problem", The Mathematical Intelligencer, 32 (2): 41–48, doi:10.1007/s00283-009-9120-4, MR 2657999, S2CID 122588849
Bollobás, Béla (1998), Modern Graph Theory, Graduate Texts in Mathematics, vol. 184, Springer-Verlag, New York, p. 23, doi:10.1007/978-1-4612-0619-4, ISBN 0-387-98488-7, MR 1633290
Harary, Frank (1960), "Some historical and intuitive aspects of graph theory", SIAM Review, 2 (2): 123–131, Bibcode:1960SIAMR...2..123H, doi:10.1137/1002023, MR 0111698
Ayres, W. L. (1938), "Some elementary aspects of topology", The American Mathematical Monthly, 45 (2): 88–92, doi:10.1080/00029890.1938.11990773, JSTOR 2304276, MR 1524194
Harary, F. (1964), "Recent results in topological graph theory", Acta Mathematica, 15 (3–4): 405–411, doi:10.1007/BF01897149, hdl:2027.42/41775, MR 0166775, S2CID 123170864; see p. 409.
Parker, Matt (2015), Things to Make and Do in the Fourth Dimension: A Mathematician's Journey Through Narcissistic Numbers, Optimal Dating Algorithms, at Least Two Kinds of Infinity, and More, New York: Farrar, Straus and Giroux, pp. 180–181, 191–192, ISBN 978-0-374-53563-6, MR 3753642
Larsen, Mogens Esrom (1994), "Misunderstanding my mazy mazes may make me miserable", in Guy, Richard K.; Woodrow, Robert E. (eds.), Proceedings of the Eugène Strens Memorial Conference on Recreational Mathematics and its History held at the University of Calgary, Calgary, Alberta, August 1986, MAA Spectrum, Washington, DC: Mathematical Association of America, pp. 289–293, ISBN 0-88385-516-X, MR 1303141. See Figure 7, p. 292.
Streinu, Ileana (2005), "Pseudo-triangulations, rigidity and motion planning", Discrete & Computational Geometry, 34 (4): 587–635, doi:10.1007/s00454-005-1184-0, MR 2173930, S2CID 25281202. See p. 600: "Not all generically minimally rigid graphs have embeddings as pseudo-triangulations, because not all are planar graphs. The smallest example is $K_{3,3}$ ".
Tutte, W. T. (1947), "A family of cubical graphs", Proceedings of the Cambridge Philosophical Society, 43 (4): 459–474, Bibcode:1947PCPS...43..459T, doi:10.1017/s0305004100023720, MR 0021678, S2CID 123505185
Campbell, S. R.; Ellingham, M. N.; Royle, Gordon F. (1993), "A characterisation of well-covered cubic graphs", Journal of Combinatorial Mathematics and Combinatorial Computing, 13: 193–212, MR 1220613
Little, Charles H. C. (1976), "A theorem on planar graphs", in Casse, Louis R. A.; Wallis, Walter D. (eds.), Combinatorial Mathematics IV: Proceedings of the Fourth Australian Conference Held at the University of Adelaide August 27–29, 1975, Lecture Notes in Mathematics, vol. 560, Springer, pp. 136–141, doi:10.1007/BFb0097375, MR 0427121

archive.org

Dudeney, Henry (1917), "Problem 251 – Water, Gas, and Electricity", Amusements in mathematics, vol. 100, Thomas Nelson, p. 73, Bibcode:1917Natur.100..302., doi:10.1038/100302a0, S2CID 10245524. The solution given on pp. 200–201 involves passing a line through one of the other houses.
Dudeney, Henry (1913), "Perplexities, with some easy puzzles for beginners", The Strand Magazine, vol. 46, p. 110
Henneberg, L. (1908), "Die graphische Statik der starren Körper", Encyklopädie der Mathematischen Wissenschaften, vol. 4, pp. 345–434. See in particular p. 403.
Thomsen, Julius (July 1886), "Die Constitution des Benzols" (PDF), Berichte der Deutschen Chemischen Gesellschaft, 19 (2): 2944–2950, doi:10.1002/cber.188601902285

books.google.com

"Puzzle", Successful Farming, vol. 13, p. 50, 1914; "A well and house puzzle", The Youth's Companion, vol. 90, no. 2, p. 392, 1916.
"32. The fountain puzzle", The Magician's Own Book, Or, The Whole Art of Conjuring, New York: Dick & Fitzgerald, 1857, p. 276
Loyd, Sam (1959), "82: The Quarrelsome Neighbors", in Gardner, Martin (ed.), Mathematical Puzzles of Sam Loyd, Dover Books, p. 79, ISBN 9780486204987
Bollobás, Béla (1998), Modern Graph Theory, Graduate Texts in Mathematics, vol. 184, Springer-Verlag, New York, p. 23, doi:10.1007/978-1-4612-0619-4, ISBN 0-387-98488-7, MR 1633290
Kappraff, Jay (2001), Connections: The Geometric Bridge Between Art and Science, K & E Series on Knots and Everything, vol. 25, World Scientific, p. 128, ISBN 9789810245863
O’Beirne, T. H. (December 21, 1961), "Christmas puzzles and paradoxes, 51: For boys, men and heroes", New Scientist, vol. 12, no. 266, pp. 751–753
Larsen, Mogens Esrom (1994), "Misunderstanding my mazy mazes may make me miserable", in Guy, Richard K.; Woodrow, Robert E. (eds.), Proceedings of the Eugène Strens Memorial Conference on Recreational Mathematics and its History held at the University of Calgary, Calgary, Alberta, August 1986, MAA Spectrum, Washington, DC: Mathematical Association of America, pp. 289–293, ISBN 0-88385-516-X, MR 1303141. See Figure 7, p. 292.

doi.org

Gries, David; Schneider, Fred B. (1993), "Chapter 19: A theory of graphs", A Logical Approach to Discrete Math, New York: Springer, pp. 423–460, doi:10.1007/978-1-4757-3837-7, ISBN 978-1-4419-2835-1, S2CID 206657798. See p. 437: " $K_{3,3}$ is known as the utility graph".
Kullman, David (1979), "The utilities problem", Mathematics Magazine, 52 (5): 299–302, doi:10.1080/0025570X.1979.11976807, JSTOR 2689782
Dudeney, Henry (1917), "Problem 251 – Water, Gas, and Electricity", Amusements in mathematics, vol. 100, Thomas Nelson, p. 73, Bibcode:1917Natur.100..302., doi:10.1038/100302a0, S2CID 10245524. The solution given on pp. 200–201 involves passing a line through one of the other houses.
Beineke, Lowell; Wilson, Robin (2010), "The early history of the brick factory problem", The Mathematical Intelligencer, 32 (2): 41–48, doi:10.1007/s00283-009-9120-4, MR 2657999, S2CID 122588849
Thomsen, Julius (July 1886), "Die Constitution des Benzols" (PDF), Berichte der Deutschen Chemischen Gesellschaft, 19 (2): 2944–2950, doi:10.1002/cber.188601902285
Bollobás, Béla (1998), Modern Graph Theory, Graduate Texts in Mathematics, vol. 184, Springer-Verlag, New York, p. 23, doi:10.1007/978-1-4612-0619-4, ISBN 0-387-98488-7, MR 1633290
Harary, Frank (1960), "Some historical and intuitive aspects of graph theory", SIAM Review, 2 (2): 123–131, Bibcode:1960SIAMR...2..123H, doi:10.1137/1002023, MR 0111698
Kuratowski, Kazimierz (1930), "Sur le problème des courbes gauches en topologie" (PDF), Fundamenta Mathematicae (in French), 15: 271–283, doi:10.4064/fm-15-1-271-283
Ayres, W. L. (1938), "Some elementary aspects of topology", The American Mathematical Monthly, 45 (2): 88–92, doi:10.1080/00029890.1938.11990773, JSTOR 2304276, MR 1524194
Harary, F. (1964), "Recent results in topological graph theory", Acta Mathematica, 15 (3–4): 405–411, doi:10.1007/BF01897149, hdl:2027.42/41775, MR 0166775, S2CID 123170864; see p. 409.
Streinu, Ileana (2005), "Pseudo-triangulations, rigidity and motion planning", Discrete & Computational Geometry, 34 (4): 587–635, doi:10.1007/s00454-005-1184-0, MR 2173930, S2CID 25281202. See p. 600: "Not all generically minimally rigid graphs have embeddings as pseudo-triangulations, because not all are planar graphs. The smallest example is $K_{3,3}$ ".
Tutte, W. T. (1947), "A family of cubical graphs", Proceedings of the Cambridge Philosophical Society, 43 (4): 459–474, Bibcode:1947PCPS...43..459T, doi:10.1017/s0305004100023720, MR 0021678, S2CID 123505185
Little, Charles H. C. (1976), "A theorem on planar graphs", in Casse, Louis R. A.; Wallis, Walter D. (eds.), Combinatorial Mathematics IV: Proceedings of the Fourth Australian Conference Held at the University of Adelaide August 27–29, 1975, Lecture Notes in Mathematics, vol. 560, Springer, pp. 136–141, doi:10.1007/BFb0097375, MR 0427121

handle.net

hdl.handle.net

Harary, F. (1964), "Recent results in topological graph theory", Acta Mathematica, 15 (3–4): 405–411, doi:10.1007/BF01897149, hdl:2027.42/41775, MR 0166775, S2CID 123170864; see p. 409.

harvard.edu

ui.adsabs.harvard.edu

Dudeney, Henry (1917), "Problem 251 – Water, Gas, and Electricity", Amusements in mathematics, vol. 100, Thomas Nelson, p. 73, Bibcode:1917Natur.100..302., doi:10.1038/100302a0, S2CID 10245524. The solution given on pp. 200–201 involves passing a line through one of the other houses.
Harary, Frank (1960), "Some historical and intuitive aspects of graph theory", SIAM Review, 2 (2): 123–131, Bibcode:1960SIAMR...2..123H, doi:10.1137/1002023, MR 0111698
Tutte, W. T. (1947), "A family of cubical graphs", Proceedings of the Cambridge Philosophical Society, 43 (4): 459–474, Bibcode:1947PCPS...43..459T, doi:10.1017/s0305004100023720, MR 0021678, S2CID 123505185

icm.edu.pl

matwbn.icm.edu.pl

Kuratowski, Kazimierz (1930), "Sur le problème des courbes gauches en topologie" (PDF), Fundamenta Mathematicae (in French), 15: 271–283, doi:10.4064/fm-15-1-271-283

jstor.org

Kullman, David (1979), "The utilities problem", Mathematics Magazine, 52 (5): 299–302, doi:10.1080/0025570X.1979.11976807, JSTOR 2689782
Ayres, W. L. (1938), "Some elementary aspects of topology", The American Mathematical Monthly, 45 (2): 88–92, doi:10.1080/00029890.1938.11990773, JSTOR 2304276, MR 1524194

semanticscholar.org

api.semanticscholar.org

Gries, David; Schneider, Fred B. (1993), "Chapter 19: A theory of graphs", A Logical Approach to Discrete Math, New York: Springer, pp. 423–460, doi:10.1007/978-1-4757-3837-7, ISBN 978-1-4419-2835-1, S2CID 206657798. See p. 437: " $K_{3,3}$ is known as the utility graph".
Dudeney, Henry (1917), "Problem 251 – Water, Gas, and Electricity", Amusements in mathematics, vol. 100, Thomas Nelson, p. 73, Bibcode:1917Natur.100..302., doi:10.1038/100302a0, S2CID 10245524. The solution given on pp. 200–201 involves passing a line through one of the other houses.
Beineke, Lowell; Wilson, Robin (2010), "The early history of the brick factory problem", The Mathematical Intelligencer, 32 (2): 41–48, doi:10.1007/s00283-009-9120-4, MR 2657999, S2CID 122588849
Harary, F. (1964), "Recent results in topological graph theory", Acta Mathematica, 15 (3–4): 405–411, doi:10.1007/BF01897149, hdl:2027.42/41775, MR 0166775, S2CID 123170864; see p. 409.
Streinu, Ileana (2005), "Pseudo-triangulations, rigidity and motion planning", Discrete & Computational Geometry, 34 (4): 587–635, doi:10.1007/s00454-005-1184-0, MR 2173930, S2CID 25281202. See p. 600: "Not all generically minimally rigid graphs have embeddings as pseudo-triangulations, because not all are planar graphs. The smallest example is $K_{3,3}$ ".
Tutte, W. T. (1947), "A family of cubical graphs", Proceedings of the Cambridge Philosophical Society, 43 (4): 459–474, Bibcode:1947PCPS...43..459T, doi:10.1017/s0305004100023720, MR 0021678, S2CID 123505185

uibk.ac.at

geometrie.uibk.ac.at

Walter, D.; Husty, M. L. (2007), "On a nine-bar linkage, its possible configurations and conditions for paradoxical mobility" (PDF), in Merlet, Jean-Pierre; Dahan, Marc (eds.), 12th World Congress on Mechanism and Machine Science (IFToMM 2007), International Federation for the Promotion of Mechanism and Machine Science

uni-goettingen.de

gdz.sub.uni-goettingen.de

Dixon, A. C. (1899), "On certain deformable frameworks", Messenger of Mathematics, 29: 1–21, JFM 30.0622.02

zbmath.org

Dixon, A. C. (1899), "On certain deformable frameworks", Messenger of Mathematics, 29: 1–21, JFM 30.0622.02