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@Inbook{Heule2016,
author="Heule, Marijn J. H.
and Kullmann, Oliver
and Marek, Victor W.",
editor="Creignou, Nadia
and Le Berre, Daniel",
title="Solving and Verifying the Boolean Pythagorean Triples Problem via Cube-and-Conquer",
bookTitle="Theory and Applications of Satisfiability Testing -- SAT 2016: 19th International Conference, Bordeaux, France, July 5-8, 2016, Proceedings",
year="2016",
publisher="Springer International Publishing",
address="Cham",
pages="228--245",
isbn="978-3-319-40970-2",
doi="10.1007/978-3-319-40970-2_15",
url="http://dx.doi.org/10.1007/978-3-319-40970-2_15"
}
@article{Schur1917,
author = "Schur, Issai",
title = "{\"{U}}ber die {K}ongruenz $x^m + y^m = z^m \pmod p$ ",
journal = "Jahresbericht der Deutschen Mathematikervereinigung",
volume = "25",
year = "1917",
pages = "114--117"
}
@inproceedings{LPAR23,
author = {Peter Oostema and Ruben Martins and Marijn Heule},
title = {Coloring Unit-Distance Strips using SAT},
booktitle = {LPAR23. LPAR-23: 23rd International Conference on Logic for Programming, Artificial Intelligence and Reasoning},
editor = {Elvira Albert and Laura Kovacs},
series = {EPiC Series in Computing},
volume = {73},
pages = {373--389},
year = {2020},
publisher = {EasyChair},
bibsource = {EasyChair, https://easychair.org},
issn = {2398-7340},
url = {https://easychair.org/publications/paper/69T4},
doi = {10.29007/btmj}}
@article{SanchezFlores54,
title={On tournaments free of large transitive subtournaments},
author={Sanchez-Flores, Adolfo},
journal={Graphs and Combinatorics},
volume={14},
number={2},
pages={181--200},
year={1998},
publisher={Springer}
}
@article{SanchezFlores55,
title={On tournaments and their largest transitive subtournaments},
author={Sanchez-Flores, Adolfo},
journal={Graphs and Combinatorics},
volume={10},
number={2-4},
pages={367--376},
year={1994},
publisher={Springer}
}
@book{Moon,
title={Topics on tournaments in graph theory},
author={Moon, John W},
year={2015},
publisher={Courier Dover Publications}
}
@misc{McKay,
title = {Digraphs},
howpublished = {\url{http://users.cecs.anu.edu.au/~bdm/data/digraphs.html}},
author = {McKay, Brendan},
note = {Accessed: 2019-09-30}
}
@article{ErdosMoser,
title={On the representation of directed graphs as unions of orderings},
author={Erd\H{o}s, Paul and Moser, Leo},
journal={Math. Inst. Hung. Acad. Sci},
volume={9},
pages={125--132},
year={1964}
}
@article{DBLP:journals/dam/Gelder08,
author = {Allen Van Gelder},
title = {Another look at graph coloring via propositional satisfiability},
journal = {Discrete Applied Mathematic},
volume = {156},
number = {2},
pages = {230--243},
year = {2008}
}
@misc{coloring-urls,
author = {Jaan Parts},
title = {Blog post on Polymath16},
howpublished = "\url{https://dustingmixon.wordpress.com/2018/08/28/polymath16-tenth-thread-open-sat-instances/#comment-5488}",
year = {2018},
note = "[Online; accessed 21-February-2020]"
}
@article{Jaan509,
title={Graph minimization, focusing on the example of 5-chromatic
unit-distance graphs in the plane},
author={Jaan Parts},
year={2020},
issue={4},
volume={29},
journal={Geombinatorics},
}
@misc{Alexeev,
author = {Boris Alexeev},
title = {Blog post on Polymath16},
howpublished = "\url{https://dustingmixon.wordpress.com/2018/06/16/polymath16-seventh-thread-upper-bounds/#comment-4827}",
year = {2018},
note = "[Online; accessed 23-April-2020]"
}
@inproceedings{POS-18:Effect_of_Scrambling_CNFs,
author = {Armin Biere and Marijn Heule},
title = {{The Effect of Scrambling CNFs}},
booktitle = {Proceedings of Pragmatics of SAT 2015 and 2018},
editor = {Daniel Le Berre and Matti J\"arvisalo},
series = {EPiC Series in Computing},
volume = {59},
pages = {111--126},
year = {2019},
publisher = {EasyChair},
bibsource = {EasyChair, https://easychair.org},
issn = {2398-7340},
url = {https://easychair.org/publications/paper/HtqQ},
doi = {10.29007/9dj5}}
@InProceedings{CP19,
author="Heule, Marijn J. H.",
editor="Schiex, Thomas
and de Givry, Simon",
title="Trimming Graphs Using Clausal Proof Optimization",
booktitle="Principles and Practice of Constraint Programming",
year="2019",
publisher="Springer International Publishing",
address="Cham",
pages="251--267",
}
@article{Pritikin,
title = "All Unit-Distance Graphs of Order 6197 Are 6-Colorable",
journal = "Journal of Combinatorial Theory, Series B",
volume = "73",
number = "2",
pages = "159 - 163",
year = "1998",
issn = "0095-8956",
author = "Dan Pritikin",
}
@article{coloring-bounds,
author = {Maria Axenovich and
JiHyeok Choi and
Michelle A. Lastrina and
T. McKay and
J. Smith and
B. Stanton},
title = {On the Chromatic Number of Subsets of the Euclidean Plane},
journal = {Graphs and Combinatorics},
volume = {30},
number = {1},
pages = {71--81},
year = {2014},
url = {https://doi.org/10.1007/s00373-012-1249-9},
doi = {10.1007/s00373-012-1249-9},
timestamp = {Sat, 27 May 2017 14:22:52 +0200},
biburl = {https://dblp.org/rec/bib/journals/gc/AxenovichCLMSS14},
bibsource = {dblp computer science bibliography, https://dblp.org}
}
@article{epsilon-coloring,
author = {Felix Bock},
title = { Epsilon-colorings of strips},
journal = {Acta Mathematica Universitatis Comenianae},
volume = {88},
number = {3},
year = {2019}
}
@article{bauslaugh1998tearing,
title={Tearing a strip off the plane},
author={Bauslaugh, Bruce L},
journal={Journal of Graph Theory},
volume={29},
number={1},
pages={17--33},
year={1998},
publisher={Wiley Online Library}
}
@inproceedings{heule17_shortproofs,
title = {Short Proofs Without New Variables},
author = {Heule, Marijn J. H. and
Kiesl, Benjamin and
Biere, Armin},
year = {2017},
booktitle = {Proc.\ of the 26th Int.\ Conference on Automated Deduction (CADE-26)},
pages = {130--147},
editor = {Leonardo de Moura},
publisher = {Springer},
series = {LNCS},
volume = {10395},
address = {Heidelberg}
}
@article{deconstruct,
title={Locating Minimal Infeasible Constraint Sets in Linear Programs},
author={Chinneck, John W. and Dravnieks, Erik W.},
journal={INFORMS Journal on Computing},
volume={3},
issue={2},
year={1991},
pages={157--168},
}
@phdthesis{Zhang:2003,
author = {Zhang, Lintao},
advisor = {Malik, Sharad},
title = {Searching for Truth: Techniques for Satisfiability of Boolean Formulas},
year = {2003},
school = {Princeton University},
address = {Princeton, NJ, USA},
}
@InProceedings{SMUS1,
author="Ignatiev, Alexey
and Previti, Alessandro
and Liffiton, Mark
and Marques-Silva, Joao",
editor="Pesant, Gilles",
title="Smallest MUS Extraction with Minimal Hitting Set Dualization",
booktitle="Principles and Practice of Constraint Programming",
year="2015",
publisher="Springer International Publishing",
address="Cham",
pages="173--182",
}
@Article{SMUS2,
author="Liffiton, Mark
and Mneimneh, Maher
and Lynce, In{\^e}s
and Andraus, Zaher
and Marques-Silva, Jo{\~a}o
and Sakallah, Karem",
title="A branch and bound algorithm for extracting smallest minimal unsatisfiable subformulas",
journal="Constraints",
year="2008",
month="Aug",
day="05",
volume="14",
number="4",
pages="415",
}
@InProceedings{SMUS3,
author="Mneimneh, Maher
and Lynce, In{\^e}s
and Andraus, Zaher
and Marques-Silva, Jo{\~a}o
and Sakallah, Karem",
editor="Bacchus, Fahiem
and Walsh, Toby",
title="A Branch-and-Bound Algorithm for Extracting Smallest Minimal Unsatisfiable Formulas",
booktitle="Theory and Applications of Satisfiability Testing",
year="2005",
publisher="Springer Berlin Heidelberg",
address="Berlin, Heidelberg",
pages="467--474",
}
@article{Hadwiger1950,
author="Hadwiger, H.",
title="Minkowskische Addition und Subtraktion beliebiger Punktmengen und die Theoreme von Erhard Schmidt",
journal="Mathematische Zeitschrift",
year="1950",
month="Jun",
day="01",
volume="53",
number="3",
pages="210--218",
issn="1432-1823",
}
@article{Geo,
author={Heule, Marijn J. H.},
year={2018},
title={Computing Small Unit-Distance Graphs with Chromatic Number 5},
journal={Geombinatorics},
volume={XXVIII},
issue={1},
pages={32-50},
}
@inproceedings{MUS2004,
author = {In{\^{e}}s Lynce and
Marques Silva, Jo{\~{a}}o P.},
title = {On Computing Minimum Unsatisfiable Cores},
booktitle = {{SAT} 2004 - The Seventh International Conference on Theory and Applications
of Satisfiability Testing, 10-13 May 2004, Vancouver, BC, Canada,
Online Proceedings},
year = {2004},
crossref = {DBLP:conf/sat/2004},
timestamp = {Tue, 10 Jan 2006 08:26:54 +0100},
biburl = {https://dblp.org/rec/bib/conf/sat/LynceM04},
bibsource = {dblp computer science bibliography, https://dblp.org}
}
@inproceedings{MUS2011,
author = {Marques-Silva, Joao and Lynce, Ines},
title = {On Improving MUS Extraction Algorithms},
booktitle = {Proceedings of the 14th International Conference on Theory and Application of Satisfiability Testing},
series = {SAT'11},
year = {2011},
isbn = {978-3-642-21580-3},
location = {Ann Arbor, MI},
pages = {159--173},
numpages = {15},
acmid = {2023493},
publisher = {Springer-Verlag},
address = {Berlin, Heidelberg},
}
@inproceedings{MUS2014,
author = {Anton Belov and
Marijn Heule and
Jo{\~{a}}o Marques{-}Silva},
title = {{MUS} Extraction Using Clausal Proofs},
booktitle = {Theory and Applications of Satisfiability Testing - {SAT} 2014},
pages = {48--57},
year = {2014},
crossref = {DBLP:conf/sat/2014},
}
@proceedings{DBLP:conf/sat/2014,
editor = {Carsten Sinz and
Uwe Egly},
title = {Theory and Applications of Satisfiability Testing - {SAT} 2014},
series = {Lecture Notes in Computer Science},
volume = {8561},
publisher = {Springer},
year = {2014},
}
@proceedings{DBLP:conf/sat/2004,
title = {{SAT} 2004 - The Seventh International Conference on Theory and Applications
of Satisfiability Testing, 10-13 May 2004, Vancouver, BC, Canada,
Online Proceedings},
year = {2004},
timestamp = {Mon, 06 Jun 2005 13:58:12 +0200},
biburl = {https://dblp.org/rec/bib/conf/sat/2004},
bibsource = {dblp computer science bibliography, https://dblp.org}
}
@inproceedings{RitircBiereKauers-SCSC18,
author = {Daniela Ritirc and Armin Biere and Manuel Kauers},
title = {A Practical Polynomial Calculus for Arithmetic Circuit Verification},
booktitle = {3rd International Workshop on Satisfiability Checking and Symbolic Computation},
note = {To appear},
year = {2018},
}
@BOOK{GJ73,
author = "Garey, Michael R., and Johnson, David S.",
title = "A Guide to the Theory of the NP-Completeness",
publisher = "W. H. Freeman and Company",
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year = 1979,
}
@article{deBruijn,
author={de Bruijn, N. G. and Erd\H{o}s, Paul},
year = {1951},
title = {A colour problem for infinite graphs and a problem in the theory of relations},
journal = {Nederl. Akad. Wetensch. Proc. Ser. A},
volume = {54},
pages = {371--373},
}
@book{coloring,
affiliation = {College of Letters Arts and Sciences, University of Colorado at Colorado Springs},
author = {Soifer, Alexander},
isbn = {978-0-387-74640-1},
publisher = {Springer New York},
title = {The Mathematical Coloring Book},
year = {2009}
}
@book{Singular,
author = {Greuel, Gert-Martin and Pfister, Gerhard},
title = {A Singular Introduction to Commutative Algebra},
year = {2007},
isbn = {3540735410, 9783540735410},
edition = {2nd},
publisher = {Springer},
}
[download]
@inproceedings{ijcai2017-98,
author = {Mao Luo and
Chu{-}Min Li and
Fan Xiao and
Felip Many{\`{a}} and
Zhipeng L{\"{u}}},
title = {An Effective Learnt Clause Minimization Approach for {CDCL} {SAT} Solvers},
booktitle = {Proceedings of the Twenty-Sixth International Joint Conference on
Artificial Intelligence, {IJCAI-17}},
pages = {703--711},
year = {2017},
doi = {10.24963/ijcai.2017/98},
}
@inproceedings{rat,
author="Heule, Marijn J. H. and {Hunt Jr.}, Warren A. and Wetzler, Nathan D.",
title="Verifying Refutations with Extended Resolution",
bookTitle="Automated Deduction -- CADE-24",
year="2013",
publisher="Springer Berlin Heidelberg",
pages="345--359",
}
@misc{Cooper1344,
author = {Joshua Cooper and Chris Poirel},
title = {Note on the {P}ythagorean Triple System},
year = {2008},
url= {\url{http://www.math.sc.edu/?cooper/pth.pdf}},
}
@PHDTHESIS{Myers2015,
author = {Myers, Kellen John},
school= {Rutgers University},
title = {Computational advances in Rado numbers},
year = {2015},
}
@article{WS4,
author={Blanchard, Peter F. and Harary, Frank and Reis, Rog\'erio},
title={Partitions into sum-free sets},
journal={Integers},
volume={6},
note={\#{}A07},
year={2006},
}
@inproceedings{glucose,
author = {Gilles Audemard and
Laurent Simon},
title = {Predicting Learnt Clauses Quality in Modern {SAT} Solvers},
booktitle = {21st International Joint Conference on Artificial Intelligence},
pages = {399--404},
year = {2009},
}
@inproceedings{SC16,
author = {Balyo, Tomas and Heule, Marijn J. H. and J\"arvisalo, Matti},
title={SAT Competition 2016: Recent Developments},
booktitle={AAAI 2017},
pages= {5061--5063},
year={2017},
}
@Inbook{Heule2015,
author="Heule, Marijn J. H. and {Hunt Jr.}, Warren A. and Wetzler, Nathan D.",
title="Expressing Symmetry Breaking in DRAT Proofs",
bookTitle="Automated Deduction -- CADE-25",
year="2015",
publisher="Springer International Publishing",
pages="591--606",
}
@inproceedings{Crawford,
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