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121.
122.
The following results are obtained. (i) Let p, d, and k be fixed positive integers, and let G be a graph whose vertex set can be partitioned into parts V1, V2,…, Va such that for each i at most d vertices in V1 … Vi have neighbors in Vi+1 and r(Kk, Vi) p | V(G) |, where Vi denotes the subgraph of G induced by Vi. Then there exists a number c depending only on p, d, and k such that r(Kk, G)c | V(G) |. (ii) Let d be a positive integer and let G be a graph in which there is an independent set I V(G) such that each component of G−I has at most d vertices and at most two neighbors in I. Then r(G,G)c | V(G) |, where c is a number depending only on d. As a special case, r(G, G) 6 | V(G) | for a graph G in which all vertices of degree at least three are independent. The constant 6 cannot be replaced by one less than 4. 相似文献
123.
Prof. A. Charnes Prof. J. Rousseau Prof. L. Seiford 《International Journal of Game Theory》1982,11(3-4):163-174
The concepts of disruption and mollifiers ofCharnes/Rousseau/Seiford [1978] for games in characteristic function form are here extended to games in normal form. We show for a large class of games that theHarsanyi-Selten [1959] modification ofvon Neumann /Morgenstern's [1953] construction of a characteristic function for games in normal form, to take better account of “disruption” or “threat” possibilities, yields a constant mollifier. In general, it can be non-superadditive when the von Neumann-Morgenstern function is superadditive, and it also fails to take account of coalitional sizes. Our extended “homomollifier” concept does, and always yields a superadditive constant sum characteristic function. 相似文献
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G. Rousseau 《Aequationes Mathematicae》1992,43(2-3):145-155
Summary Gauss proved Seeber's Theorem, that the determinant of a reduced positive definite ternary quadratic form is at least half the product of its diagonal coefficients, by means of two determinantal identities whose origin has remained unclear. We examine Gauss's method from a general standpoint, as a method whereby, in certain circumstances, a polynomial in several variables may be shown to be non-negative on a convex polytope by representing it as a positive multilinear combination of the linear forms which determine the polytope. We show that Gauss's identities may be obtained in this manner and that the two identities can in fact be replaced by a simpler single identity which also gives Oppenheim's precise minimum for the determinant. 相似文献
127.
3-Nitro 4-alkyl (or aryl) amino pyridines were converted to 3-acetamido 4-a1ky1 (or aryl) amino (1H) pyridine-Z-ones by a catalytic hydrogenation-rearrangement in acetic acid medium. 相似文献
128.
A formula is found for the maximum number of edges in a graph G ? K(a, b) which contains no path P2l for l > c. A similar formula is found for the maximum number of edges in G ? K(a, b) containing no P2l + 1 for l > c. In addition, all extremal graphs are determined. 相似文献
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Jean-Marc Rousseau Gilbert Laporte 《The Journal of the Operational Research Society》1977,28(1):33-35
A scheduling problem in an outpatient clinic is considered. First the system is represented by means of a simple queueing model. The problem of minimising the patients' total queueing time is then formulated as a non-linear program and solved by applying the Kuhn-Tucker conditions. The results obtained enable the person who manages the appointment system to allocate appointment dates to patients who have different priorities. 相似文献