A polynomial-time algorithm for near-unanimity graphs

We present a simple polynomial-time algorithm that recognises reflexive, symmetric graphs admitting a near-unanimity operation. Several other characterisations of these graphs are also presented.

[1]  Hans-Jürgen Bandelt,et al.  An algebraic setting for near-unanimity consensus , 1990 .

[2]  Claude Tardif,et al.  A discrete homotopy theory for binary reflexive structures , 2004 .

[3]  Tomás Feder Classification of Homomorphisms to Oriented Cycles and of k-Partite Satisfiability , 2001, SIAM J. Discret. Math..

[4]  Cynthia Loten Retractions of chordal and related graphs , 2003 .

[5]  László Zádori Monotone Jónsson operations and near unanimity functions , 1995 .

[6]  Benoît Larose,et al.  Algebraic properties and dismantlability of finite posets , 1997, Discret. Math..

[7]  MIKLÓS MARÓTI ON THE (UN)DECIDABILITY OF A NU-TERM , 2006 .

[8]  B. Larose,et al.  Finite posets and topological spaces in locally finite varieties , 2005 .

[9]  Peter Winkler,et al.  Gibbs Measures and Dismantlable Graphs , 2000, J. Comb. Theory, Ser. B.

[10]  Hans-Jürgen Bandelt,et al.  Graphs with edge-preserving majority functions , 1992, Discret. Math..

[11]  Maurice Pouzet,et al.  Retracts: graphs and ordered sets from the metric point of view , 1986 .

[12]  Martin C. Cooper,et al.  Constraints, Consistency and Closure , 1998, Artif. Intell..

[13]  Rina Dechter,et al.  From Local to Global Consistency , 1990, Artif. Intell..

[14]  László Zádori Relational Sets and Categorical Equivalence of Algebras , 1997, Int. J. Algebra Comput..

[15]  Gábor Tardos A maximal clone of monotone operations which is not finitely generated , 1986 .

[16]  Peter Winkler,et al.  Vertex-to-vertex pursuit in a graph , 1983, Discret. Math..

[17]  Andrei A. Krokhin,et al.  First-order definable retraction problems for posets and reflexive graphs , 2004, Proceedings of the 19th Annual IEEE Symposium on Logic in Computer Science, 2004..

[18]  Aleit Mitschke Near unanimity identities and congruence distributivity in equational classes , 1978 .

[19]  Gábor Kun,et al.  Order Varieties and Monotone Retractions of Finite Posets , 2001, Order.

[20]  D. Hobby,et al.  The structure of finite algebras , 1988 .

[21]  Tomás Feder,et al.  The Computational Structure of Monotone Monadic SNP and Constraint Satisfaction: A Study through Datalog and Group Theory , 1999, SIAM J. Comput..

[22]  Kalle Kaarli,et al.  Polynomial Completeness in Algebraic Systems , 2000 .

[23]  Brian A. Davey,et al.  Near unanimity: an obstacle to general duality theory , 1995 .

[24]  Richard J. Nowakowski,et al.  The smallest graph variety containing all paths , 1983, Discret. Math..

[25]  K. A. Baker,et al.  Polynomial interpolation and the Chinese Remainder Theorem for algebraic systems , 1975 .