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2006 | 14 | 4 | 187-206
Tytuł artykułu

Recognizing Chordal Graphs: Lex BFS and MCS1

Treść / Zawartość
Warianty tytułu
Języki publikacji
EN
Abstrakty
EN
We are formalizing the algorithm for recognizing chordal graphs by lexicographic breadth-first search as presented in [13, Section 3 of Chapter 4, pp. 81-84]. Then we follow with a formalization of another algorithm serving the same end but based on maximum cardinality search as presented by Tarjan and Yannakakis [25].This work is a part of the MSc work of the first author under supervision of the second author. We would like to thank one of the anonymous reviewers for very useful suggestions.
Słowa kluczowe
Wydawca
Rocznik
Tom
14
Numer
4
Strony
187-206
Opis fizyczny
Daty
wydano
2006-01-01
online
2008-06-13
Twórcy
  • University of Alberta, Edmonton, Canada
  • University of Alberta, Edmonton, Canada
Bibliografia
  • [1] Broderick Arneson and Piotr Rudnicki. Chordal graphs. Formalized Mathematics, 14(3):79-92, 2006.
  • [2] Grzegorz Bancerek. Cardinal numbers. Formalized Mathematics, 1(2):377-382, 1990.
  • [3] Grzegorz Bancerek. The fundamental properties of natural numbers. Formalized Mathematics, 1(1):41-46, 1990.
  • [4] Grzegorz Bancerek. The ordinal numbers. Formalized Mathematics, 1(1):91-96, 1990.
  • [5] Grzegorz Bancerek and Krzysztof Hryniewiecki. Segments of natural numbers and finite sequences. Formalized Mathematics, 1(1):107-114, 1990.
  • [6] Czesław Byliński. A classical first order language. Formalized Mathematics, 1(4):669-676, 1990.
  • [7] Czesław Byliński. Functions and their basic properties. Formalized Mathematics, 1(1):55-65, 1990.
  • [8] Czesław Byliński. Functions from a set to a set. Formalized Mathematics, 1(1):153-164, 1990.
  • [9] Czesław Byliński. The modification of a function by a function and the iteration of the composition of a function. Formalized Mathematics, 1(3):521-527, 1990.
  • [10] Czesław Byliński. Partial functions. Formalized Mathematics, 1(2):357-367, 1990.
  • [11] Czesław Byliński. Some basic properties of sets. Formalized Mathematics, 1(1):47-53, 1990.
  • [12] Agata Darmochwał. Finite sets. Formalized Mathematics, 1(1):165-167, 1990.
  • [13] M. Ch. Golumbic. Algorithmic Graph Theory and Perfect Graphs. Academic Press, New York, 1980.
  • [14] Jarosław Kotowicz. Monotone real sequences. Subsequences. Formalized Mathematics, 1(3):471-475, 1990.
  • [15] Gilbert Lee. Walks in Graphs. Formalized Mathematics, 13(2):253-269, 2005.
  • [16] Gilbert Lee. Weighted and Labeled Graphs. Formalized Mathematics, 13(2):279-293, 2005.
  • [17] Gilbert Lee and Piotr Rudnicki. On ordering of bags. Formalized Mathematics, 10(1):39-46, 2002.
  • [18] Gilbert Lee and Piotr Rudnicki. Alternative graph structures. Formalized Mathematics, 13(2):235-252, 2005.
  • [19] Yatsuka Nakamura, Piotr Rudnicki, Andrzej Trybulec, and Pauline N. Kawamoto. Preliminaries to circuits, I. Formalized Mathematics, 5(2):167-172, 1996.
  • [20] Takaya Nishiyama and Yasuho Mizuhara. Binary arithmetics. Formalized Mathematics, 4(1):83-86, 1993.
  • [21] Piotr Rudnicki. Little Bezout theorem (factor theorem). Formalized Mathematics, 12(1):49-58, 2004.
  • [22] Piotr Rudnicki and Andrzej Trybulec. Abian's fixed point theorem. Formalized Mathematics, 6(3):335-338, 1997.
  • [23] Piotr Rudnicki and Andrzej Trybulec. Multivariate polynomials with arbitrary number of variables. Formalized Mathematics, 9(1):95-110, 2001.
  • [24] Christoph Schwarzweller. Term orders. Formalized Mathematics, 11(1):105-111, 2003.
  • [25] R. E. Tarjan and M. Yannakakis. Simple linear-time algorithms to test chordality of graphs, test acyclicity of hypergraphs, and selectively reduce acyclic hypergraphs. SIAM J. Comput., 13(3):566-579, 1984.
  • [26] Andrzej Trybulec. Subsets of complex numbers. To appear in Formalized Mathematics.
  • [27] Andrzej Trybulec. Domains and their Cartesian products. Formalized Mathematics, 1(1):115-122, 1990.
  • [28] Andrzej Trybulec. Tarski Grothendieck set theory. Formalized Mathematics, 1(1):9-11, 1990.
  • [29] Andrzej Trybulec. Many-sorted sets. Formalized Mathematics, 4(1):15-22, 1993.
  • [30] Andrzej Trybulec. On the sets inhabited by numbers. Formalized Mathematics, 11(4):341-347, 2003.
  • [31] Wojciech A. Trybulec. Pigeon hole principle. Formalized Mathematics, 1(3):575-579, 1990.
  • [32] Zinaida Trybulec. Properties of subsets. Formalized Mathematics, 1(1):67-71, 1990.
  • [33] Edmund Woronowicz. Relations and their basic properties. Formalized Mathematics, 1(1):73-83, 1990.
  • [34] Edmund Woronowicz. Relations defined on sets. Formalized Mathematics, 1(1):181-186, 1990.
  • [35] Edmund Woronowicz and Anna Zalewska. Properties of binary relations. Formalized Mathematics, 1(1):85-89, 1990.
Typ dokumentu
Bibliografia
Identyfikatory
Identyfikator YADDA
bwmeta1.element.doi-10_2478_v10037-006-0022-z
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