Geodesic
On universal graphs for hom-properties
Discussiones Mathematicae. Graph Theory, Tome 29 (2009) no. 2, pp. 401-409.

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A graph property is any isomorphism closed class of simple graphs. For a simple finite graph H, let → H denote the class of all simple countable graphs that admit homomorphisms to H, such classes of graphs are called hom-properties. Given a graph property , a graph G ∈ is universal in if each member of is isomorphic to an induced subgraph of G. In particular, we consider universal graphs in → H and we give a new proof of the existence of a universal graph in → H, for any finite graph H.
Keywords: universal graph, weakly universal graph, hom-property, core 
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Mihók, Peter; Miškuf, Jozef; Semanišin, Gabriel. On universal graphs for hom-properties. Discussiones Mathematicae. Graph Theory, Tome 29 (2009) no. 2, pp. 401-409. http://geodesic.mathdoc.fr/item/DMGT_2009_29_2_a13/

[1] A. Bonato, A family of universal pseudo-homogeneous G-colourable graphs, Discrete Math. 247 (2002) 13-23, doi: 10.1016/S0012-365X(01)00158-3.

[2] A. Bonato, Homomorphisms and amalgamation, Discrete Math. 270 (2003) 33-42, doi: 10.1016/S0012-365X(02)00864-6.

[3] A. Bonato, A Course on the Web Graph, Graduate Studies in Mathematics, Volume 89, AMS (2008) ISBN 978-0-8218-4467-0.

[4] M. Borowiecki, I. Broere, M. Frick, P. Mihók and G. Semanišin, Survey of Hereditary Properties of Graphs, Discuss. Math. Graph Theory 17 (1997) 5-50, doi: 10.7151/dmgt.1037.

[5] P.J. Cameron, The random graph, in: R.L. Graham, J. Nesetril (eds.), Algorithms and Combinatorics 14 (Springer, New York, 1997).

[6] G. Cherlin, S. Shelah and N. Shi, Universal Graphs with Forbidden Subgraphs and Algebraic Closure, Advances in Applied Mathematics 22 (1999) 454-491, doi: 10.1006/aama.1998.0641.

[7] R. Cowen, S.H. Hechler and P. Mihók, Graph coloring compactness theorems equivalent to BPI, Scientia Math. Japonicae 56 (2002) 171-180.

[8] R.L. Graham, M. Grötschel and L. Lovász, Handbook of Combinatorics (Elsevier Science B.V. Amsterdam, 1995).

[9] P. Hell and J. Nesetril, The core of a graph, Discrete Math. 109 (1992) 117-126, doi: 10.1016/0012-365X(92)90282-K.

[10] P. Hell and J. Nesetril, Graphs and Homomorphisms, Oxford Lecture Series In Mathematics and its Applications 28 (Oxford University Press, 2004).

[11] P. Komjáth, Some remarks on universal graphs, Discrete Math. 199 (1999) 259-265, doi: 10.1016/S0012-365X(98)00339-2.

[12] J. Kratochví l and P. Mihók, Hom-properties are uniquely factorizable into irreducible factors, Discrete Math. 213 (2000) 189-194, doi: 10.1016/S0012-365X(99)00179-X.

[13] J. Kratochví l, P. Mihók and G. Semanišin, Graphs maximal with respect to hom-properties, Discuss. Math. Graph Theory 18 (1997) 77-88, doi: 10.7151/dmgt.1040.

[14] J. Nesetril, Graph homomorphisms and their structures, Proc. Seventh Quadrennial International Conference on the Theory and Applications of Graphs 2 (1995) 825-832.

[15] R. Rado, Universal graphs and universal functions, Acta Arith. 9 (1964) 331-340.

[16] E.R. Scheinerman, On the Structure of Hereditary Classes of Graphs, J. Graph Theory 10 (1986) 545-551, doi: 10.1002/jgt.3190100414.

[17] X. Zhu, Uniquely H-colourable graphs with large girth, J. Graph Theory 23 (1996) 33-41, doi: 10.1002/(SICI)1097-0118(199609)23:133::AID-JGT3>3.0.CO;2-L