Geodesic
On the entropy minimal hereditary classes of coloured graphs
Diskretnyj analiz i issledovanie operacij, Tome 16 (2009) no. 5, pp. 19-25 Cet article a éte moissonné depuis la source Math-Net.Ru

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We consider hereditary classes of graphs with coloured edges. The class is called entropy minimal if it does not contain proper hereditary subclasses having the same entropy value (logarithmic density). It is known for simple graphs that, for arbitrary fixed $a$ and $b$, the class consisting of all graphs admitting a partition by $a$ cliques and $b$ independent sets is entropy minimal. We prove a generalization of this statement for coloured graphs. Bibl. 5.
Keywords: hereditary class, entropy, entropy minimal class. 
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V. E. Alekseev; S. V. Sorochan. On the entropy minimal hereditary classes of coloured graphs. Diskretnyj analiz i issledovanie operacij, Tome 16 (2009) no. 5, pp. 19-25. http://geodesic.mathdoc.fr/item/DA_2009_16_5_a1/

[1] Alekseev V. E., “Oblast znachenii entropii nasledstvennykh klassov grafov”, Diskret. matematika, 4:2 (1992), 148–157 | MR | Zbl

[2] Alekseev V. E., Sorochan S. V., “Ob entropii nasledstvennykh klassov tsvetnykh grafov”, Diskret. matematika, 12:2 (2000), 99–102 | MR | Zbl

[3] Sorochan S. V., “Ob entropii kompozitsii nasledstvennykh klassov tsvetnykh grafov”, Diskret. analiz i issled. operatsii. Ser. 1, 9:1 (2002), 59–83 | MR

[4] Sorochan S. V., “O regulyarnykh kompozitsiyakh nasledstvennykh klassov tsvetnykh grafov”, Diskret. analiz i issled. operatsii. Ser. 1, 10:1 (2003), 79–104 | MR | Zbl

[5] Bollobás B., Thomason A., “Projections of bodies and hereditary properties of hypergraphs”, Bull. London Math. Soc., 27:5 (1995), 417–424 | DOI | MR | Zbl