A Conjecture on Stat. Silv. V. 3. 94

On a conjecture of V. Nikiforov

In this paper we will prove that μ(G) + μ(G) ≤ 1 + √ 3 2 n − 1 where μ(G), μ(G) are the greatest eigenvalues of the adjacency matrices of the graph G and its complement and n denotes the number of vertices of G.

Blood 94/3

Monocytes/macrophages serve as sentinels involved in chronic inflammation and the eradication of various pathogens. To define molecularly the differentiation of blood monocytes into macrophages, we conducted serial analysis of gene expression (SAGE) in human blood monocytes/ macrophages induced by granulocyte-macrophage colonystimulating factor (GM-CSF) or M-CSF. SAGE analysis of 57,560, 57,463...

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On a Conjecture of Erdos on 3-powerful Numbers

A conjecture of P. Erdos says that the diophantine equation x+y = z has infinitely many solutions with (x,y) — 1 and such that if a prime p divides xyz, then p divides xyz. In this paper, we give a proof of this conjecture. Let k ^ 2 be an integer. A /c-powerful number is a positive integer x with the property that if the prime p divides x, then p divides x (2-powerful numbers were called initi...

A note on Fouquet-Vanherpe’s question and Fulkerson conjecture

‎The excessive index of a bridgeless cubic graph $G$ is the least integer $k$‎, ‎such that $G$ can be covered by $k$ perfect matchings‎. ‎An equivalent form of Fulkerson conjecture (due to Berge) is that every bridgeless‎ ‎cubic graph has excessive index at most five‎. ‎Clearly‎, ‎Petersen graph is a cyclically 4-edge-connected snark with excessive index at least 5‎, ‎so Fouquet and Vanherpe as...