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61.
We describe two new algorithms for the generation of all non‐isomorphic cubic graphs with girth at least that are very efficient for and show how these algorithms can be restricted to generate snarks with girth at least k. Our implementation of these algorithms is more than 30, respectively 40 times faster than the previously fastest generator for cubic graphs with girth at least six and seven, respectively. Using these generators we have also generated all nonisomorphic snarks with girth at least six up to 38 vertices and show that there are no snarks with girth at least seven up to 42 vertices. We present and analyze the new list of snarks with girth 6. 相似文献
62.
图X称为弱点传递图如果X的自同态幺半群EndX在顶点集V(X)上的作用是传递的 .本文给出了广义Petersen图是二分图的充要条件 ,刻划了奇围长小于 9的广义Petersen图的弱点传递性 ,作为推论给出了所有h ≤ 1 5的弱点传递的广义Pe tersen图P(h ,t) . 相似文献
63.
In this paper we determine all elliptic curves En:y2=x3−n2x with the smallest 2-Selmer groups Sn=Sel2(En(Q))={1} and Sn′=Sel2(En′(Q))={±1,±n}(En′:y2=x3+4n2x) based on the 2-descent method. The values of n for such curves En are described in terms of graph-theory language. It is well known that the rank of the group En(Q) for such curves En is zero, the order of its Tate-Shafarevich group is odd, and such integers n are non-congruent numbers. 相似文献
64.
通过对子图和围长的研究,完全刻画了直径为3的3-正则简单平面图,获得了这类图仅有的11个非同构图. 相似文献
65.
Convex envelopes of nonconvex functions are widely used to calculate lower bounds to solutions of nonlinear programming problems (NLP), particularly within the context of spatial Branch-and-Bound methods for global optimization. This paper proposes a nonlinear continuous and differentiable convex envelope for monomial terms of odd degree, x
2k+1, where k N and the range of x includes zero. We prove that this envelope is the tightest possible. We also derive a linear relaxation from the proposed envelope, and compare both the nonlinear and linear formulations with relaxations obtained using other approaches. 相似文献
66.
Yannick Saouter. 《Mathematics of Computation》1998,67(222):863-866
Vinogradov's theorem states that any sufficiently large odd integer is the sum of three prime numbers. This theorem allows us to suppose the conjecture that this is true for all odd integers. In this paper, we describe the implementation of an algorithm which allowed us to check this conjecture up to .
67.
Jian‐Liang Wu 《Journal of Graph Theory》1999,31(2):129-134
The linear arboricity la(G) of a graph G is the minimum number of linear forests that partition the edges of G. Akiyama, Exoo, and Harary conjectured that for any simple graph G with maximum degree Δ. The conjecture has been proved to be true for graphs having Δ = 1, 2, 3, 4, 5, 6, 8, 10. Combining these results, we prove in the article that the conjecture is true for planar graphs having Δ(G) ≠ 7. Several related results assuming some conditions on the girth are obtained as well. © 1999 John Wiley & Sons, Inc. J Graph Theory 31: 129–134, 1999 相似文献
68.
Xuding Zhu 《Journal of Graph Theory》1999,30(1):1-6
We shall prove that for any graph H that is a core, if χ(G) is large enough, then H × G is uniquely H‐colorable. We also give a new construction of triangle free graphs, which are uniquely n‐colorable. © 1999 John Wiley & Sons, Inc. J Graph Theory 30: 1–6, 1999 相似文献
69.
I.IntroductionSinceII]proposedtheSlitIslandMethod(i.e.SIM)inthefractaldimensionmeasurementformetalfaultplane,alotofresearchworkhasbeendoneinthisfield,whichiswidelyusedtosolvetheproblemsinengineeringandphysics.However,manyexperimentalresultsshowthatthetana… 相似文献
70.