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On a graph packing conjecture by Bollobás, Eldridge and Catlin

✍ Scribed by Hemanshu Kaul; Alexandr Kostochka; Gexin Yu


Publisher
Springer-Verlag
Year
2008
Tongue
English
Weight
457 KB
Volume
28
Category
Article
ISSN
0209-9683

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📜 SIMILAR VOLUMES


On a conjecture of bollobás and bosák
✍ Štefan Znám 📂 Article 📅 1982 🏛 John Wiley and Sons 🌐 English ⚖ 364 KB

## Abstract It is shown that, for all sufficiently large __k__, the complete graph __K~n~__ can be decomposed into __k__ factors of diameter 2 if and only if __n__ ≥ 6__k__.

Proof of a Conjecture of Bollobás and Ko
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For any integer r \ 1, let a(r) be the largest constant a \ 0 such that if E > 0 and 0 < c < c 0 for some small c 0 =c 0 (r, E) then every graph G of sufficiently large order n and at least edges contains a copy of any (r+1)-chromatic graph H of independence number a(H) [ (a -E) log n log(1/c) .

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✍ Y. Caro; Y. Rodity 📂 Article 📅 1990 🏛 Elsevier Science 🌐 English ⚖ 212 KB

In this note we improve significantly the result appeared in [4] by showing that any sequence of trees { T2, 'I;, . , T,} can be packed into the complete bipartite graph K,\_,,n,z (n even) for f = 0.3n. Furthermore we support Fishburn's Conjecture [2] by showing that any sequence {T,, T4,