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104
Voted
CPC
2007
14 years 11 months ago
2007
We show that a random 4-regular graph asymptotically almost surely (a.a.s.) has chromatic number 3. The proof uses an efficient algorithm which a.a.s. 3colours a random 4-regular ...
CPC
2007
14 years 11 months ago
2007
We study a point process describing the asymptotic behavior of sizes of the largest components of the random graph G(n, p) in the critical window, that is, for p = n−1 + λn−4/...
96
Voted
CPC
2007
14 years 11 months ago
2007
Consider two graphs G1 and G2 on the same vertex set V and suppose that Gi has mi edges. Then there is a bipartition of V into two classes A and B so that for both i = 1, 2 we hav...
107
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CPC
2004
14 years 11 months ago
2004
The strong chromatic number, S(G), of an n-vertex graph G is the smallest number k such that after adding kn/k-n isolated vertices to G and considering any partition of the vertic...
CPC
2004
14 years 11 months ago
2004
Mader asked whether every C4-free graph G contains a subdivision of a complete graph whose order is at least linear in the average degree of G. We show that there is a subdivision...