𝔖 Bobbio Scriptorium
✦   LIBER   ✦

Multiple vertex coverings by cliques

✍ Scribed by Wayne Goddard; Michael A. Henning

Publisher
John Wiley and Sons
Year
2004
Tongue
English
Weight
99 KB
Volume
48
Category
Article
ISSN
0364-9024

No coin nor oath required. For personal study only.

✦ Synopsis

For positive integers m 1 ; . . . ; m k , let f (m 1 ; . . . ; m k ) be the minimum order of a graph whose edges can be colored with k colors such that every vertex is in a clique of cardinality m i , all of whose edges have the ith color for all i ¼ 1; 2; . . . ; k. The value for k ¼ 2 was determined by Entringer et al. (J Graph Theory 24 (1997), 21-23). We show that if k is fixed then f (m; . . . ; m) ¼ 2km À o(m). We also provide some exact values for f (m; n; 2).

📜 SIMILAR VOLUMES

Vertex coverings by monochromatic paths
Vertex coverings by monochromatic paths and cycles
✍ A. Gyárfás 📂 Article 📅 1983 🏛 John Wiley and Sons 🌐 English ⚖ 254 KB

We survey some results on covering the vertices of 2-colored complete graphs by t w o paths or by t w o cycles Qf different color. W e show the role of these results i n determining path Ramsey numbers and in algorithms for finding long monochromatic paths or cycles in 2-colored complete graphs. ##

Inside Cover: Multiplication of Human Na
Inside Cover: Multiplication of Human Natural Killer Cells by Nanosized Phosphonate-Capped Dendrimers (Angew. Chem. Int. Ed. 14/2007)
✍ Laurent Griffe; Mary Poupot; Patrice Marchand; Alexandrine Maraval; Cédric-Olivi 📂 Article 📅 2007 🏛 John Wiley and Sons 🌐 English ⚖ 35 KB 👁 2 views

**Human peripheral blood mononuclear cells** (white blood cells) cultured in the presence of dendrimers capped with phosphonate groups reveal a selective multiplication of natural killer (NK) cells. In their Communication on page 2523 ff., A.‐M. Caminade, R. Poupot, J.‐P. Majoral, and co‐workers des