On first-order definable colorings

We address the problem of characterizing H-coloring problems that are first-order definable on a fixed class of relational structures. In this context, we give also several characterizations of a homomorphism dualities arising in a class of structures.

[1]  Jaroslav Nesetril,et al.  First order properties on nowhere dense structures , 2010, The Journal of Symbolic Logic.

[2]  Detlef Seese,et al.  Monadic NP and Graph Minors , 1998, CSL.

[3]  Jaroslav Nesetril,et al.  On classes of relations and graphs determined by subobjects and factorobjects , 1978, Discret. Math..

[4]  Z. Dvořák,et al.  Asymptotical Structure of Combinatorial Objects , 2007 .

[5]  Jaroslav Nesetril,et al.  Grad and classes with bounded expansion III. Restricted graph homomorphism dualities , 2008, Eur. J. Comb..

[6]  P. Erdos,et al.  On chromatic number of graphs and set-systems , 1966 .

[7]  Zdenek Dvorak,et al.  On forbidden subdivision characterizations of graph classes , 2008, Eur. J. Comb..

[8]  Thomas J. Schaefer,et al.  The complexity of satisfiability problems , 1978, STOC.

[9]  Tomás Feder,et al.  Monotone monadic SNP and constraint satisfaction , 1993, STOC.

[10]  Jaroslav Nesetril,et al.  Graphs and homomorphisms , 2004, Oxford lecture series in mathematics and its applications.

[11]  P. Erdös,et al.  Graph Theory and Probability , 1959 .

[12]  Jaroslav Nesetril,et al.  On the complexity of H-coloring , 1990, J. Comb. Theory, Ser. B.

[13]  M. Hasse.  Zur algebraischen Begrndung der Graphentheorie. III , 1965 .

[14]  Leonid Libkin,et al.  Elements of Finite Model Theory , 2004, Texts in Theoretical Computer Science.

[15]  J. Nesetril,et al.  From Sparse Graphs to Nowhere Dense Structures: Decompositions, Independence, Dualities and Limits , 2010 .

[16]  Carsten Thomassen.  Girth in graphs , 1983, J. Comb. Theory, Ser. B.

[17]  Carsten Thomassen.  Five-Coloring Graphs on the Torus , 1994, J. Comb. Theory, Ser. B.

[18]  Phokion G. Kolaitis,et al.  On preservation under homomorphisms and unions of conjunctive queries , 2006, J. ACM.

[19]  Neil Immerman,et al.  Relational queries computable in polynomial time (Extended Abstract) , 1982, STOC '82.

[20]  Jaroslav Nesetril,et al.  Tree-depth, subgraph coloring and homomorphism bounds , 2006, Eur. J. Comb..

[21]  Anuj Dawar,et al.  Homomorphism Preservation on Quasi-Wide Classes , 2008, J. Comput. Syst. Sci..

[22]  Daniela Kühn,et al.  Every Graph of Sufficiently Large Average Degree Contains a C4-Free Subgraph of Large Average Degree , 2004, Comb..

[23]  B. Roy.  Nombre chromatique et plus longs chemins d'un graphe , 1967 .

[24]  Albert Atserias,et al.  On digraph coloring problems and treewidth duality , 2005, 20th Annual IEEE Symposium on Logic in Computer Science (LICS' 05).

[25]  Jaroslav Nesetril,et al.  Forbidden lifts (NP and CSP for combinatorialists) , 2007, Eur. J. Comb..

[26]  Jörg Flum,et al.  Finite model theory , 1995, Perspectives in Mathematical Logic.

[27]  Vojtěch Rödl.  On the chromatic number of subgraphs of a given graph , 1977 .

[28]  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..

[29]  Moshe Y. Vardi.  The complexity of relational query languages (Extended Abstract) , 1982, STOC '82.

[30]  Jaroslav Nesetril,et al.  Duality Theorems for Finite Structures (Characterising Gaps and Good Characterisations) , 2000, J. Comb. Theory, Ser. B.

[31]  Anuj Dawar,et al.  Preservation Under Extensions on Well-Behaved Finite Structures , 2005, ICALP.

[32]  Anuj Dawar,et al.  Finite Model Theory on Tame Classes of Structures , 2007, MFCS.

[33]  Jaroslav Nesetril,et al.  On nowhere dense graphs , 2011, Eur. J. Comb..

[34]  Chen C. Chang,et al.  Model Theory: Third Edition (Dover Books On Mathematics) By C.C. Chang;H. Jerome Keisler;Mathematics , 1966 .

[35]  Jaroslav Nesetril,et al.  Grad and classes with bounded expansion I. Decompositions , 2008, Eur. J. Comb..

[36]  Benjamin Rossman,et al.  Homomorphism preservation theorems , 2008, JACM.