Geodesic
Edge Partition Properties of Graphs
Canadian journal of mathematics, Tome 25 (1973) no. 3, pp. 603-610

Voir la notice de l'article provenant de la source Cambridge University Press

Erdös and Hajnal [1] have introduced an edge partition relation for graphs (1) which means that whenever the edges of G are separated into two sets, E1 and E2, there exists a subgraph G’ of G such that G’ is isomorphic to Hi and the edges of G’ are all in Ei. for i = 1 or 2. A class of graphs has the G-R (Galvin-Ramsey) property [2] if for each H in there exists a G in which satisfies G→(H,H). 
Henson, C. Ward. Edge Partition Properties of Graphs. Canadian journal of mathematics, Tome 25 (1973) no. 3, pp. 603-610. doi: 10.4153/CJM-1973-061-1
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[1] 1. Erdös, P. and Hajnal, A., On decomposition of graphs, Acta Math. Acad. Sci. Hungar. 18 (1967), 359–377. Google Scholar

[2] 2. Erdös, P. and Hajnal, A., Problems and results infinite and infinite combinatorial analysis, Ann. of New York Acad, of Sci. 175 (1970), 115–124. Google Scholar

[3] 3. Ghouila-Houri, A., Charactérisation des graphs non orientés dont on peut orienter les aretes de manière à obtenir le graph d'une relation d'ordre, C.R. Acad. Sci. Paris, Sér. A-B 254 (1962), 1370–1371. Google Scholar

[4] 4. Gilmore, P. C. and Hoffman, A. J., A characterization of comparability graphs and of interval graphs, Can. J. Math. 16 (1964), 539–548. Google Scholar

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