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《Discrete Mathematics》2020,343(12):112117
Let G be an edge-colored graph of order n. The minimum color degree of G, denoted by δc(G), is the largest integer k such that for every vertex v, there are at least k distinct colors on edges incident to v. We say that an edge-colored graph is rainbow if all its edges have different colors. In this paper, we consider vertex-disjoint rainbow triangles in edge-colored graphs. Li (2013) showed that if δc(G)(n+1)2, then G contains a rainbow triangle and the lower bound is tight. Motivated by this result, we prove that if n20 and δc(G)(n+2)2, then G contains two vertex-disjoint rainbow triangles. In particular, we conjecture that if δc(G)(n+k)2, then G contains k vertex-disjoint rainbow triangles. For any integer k2, we show that if n16k12 and δc(G)n2+k1, then G contains k vertex-disjoint rainbow triangles. Moreover, we provide sufficient conditions for the existence of k edge-disjoint rainbow triangles.  相似文献   
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The Chang-Łoś-Suszko theorem of first-order model theory characterizes universal-existential classes of models as just those elementary classes that are closed under unions of chains. This theorem can then be used to equate two model-theoretic closure conditions for elementary classes; namely unions of chains and existential substructures. In the present paper we prove a topological analogue and indicate some applications.  相似文献   
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Starch belongs to the polyglucan group. This type of polysaccharide shows a broad β-relaxation process in dielectric spectra at low temperatures, which has its molecular origin in orientational motions of sugar rings via glucosidic linkages. This chain dynamic was investigated for α(1,4)-linked starch oligomers with well-defined chain lengths of 2, 3, 4, 6, and 7 anhydroglucose units (AGUs) and for α(1,4)-polyglucans with average degrees of polymerization of 5, 10, 56, 70, and so forth (up to 3000; calculated from the mean molecular weight). The activation energy (Ea) of the segmental chain motion was lowest for dimeric maltose (Ea = 49.4 ± 1.3 kJ/mol), and this was followed by passage through a maximum at a degree of polymerization of 6 (Ea = 60.8 ± 1.8 kJ/mol). Subsequently, Ea leveled off at a value of about 52 ± 1.5 kJ/mol for chains containing more than 100 repeating units. The results were compared with the values of cellulose-like oligomers and polymers bearing a β(1,4)-linkage. Interestingly, the shape of the Ea dependency on the chain length of the molecules was qualitatively the same for both systems, whereas quantitatively the starch-like substances generally showed higher Ea values. Additionally, and for comparison, three cyclodextrins were measured by dielectric relaxation spectroscopy. The ringlike molecules, with 6, 7, and 8 α(1,4)-linked AGUs, showed moderately different types of dielectric spectra. © 2003 Wiley Periodicals, Inc. J Polym Sci Part B: Polym Phys 42: 188–197, 2004  相似文献   
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For given a graph H, a graphic sequence π = (d 1, d 2,..., d n) is said to be potentially H-graphic if there is a realization of π containing H as a subgraph. In this paper, we characterize the potentially (K 5e)-positive graphic sequences and give two simple necessary and sufficient conditions for a positive graphic sequence π to be potentially K 5-graphic, where K r is a complete graph on r vertices and K r-e is a graph obtained from K r by deleting one edge. Moreover, we also give a simple necessary and sufficient condition for a positive graphic sequence π to be potentially K 6-graphic. Project supported by National Natural Science Foundation of China (No. 10401010).  相似文献   
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Differential inequality method, bounding function method and topological degree are applied to obtain the existence criterions of at least one solution for the general fourth-order differential equations under nonlinear boundary conditions, and many existing results are complemented.  相似文献   
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一类广义Bent型S-Box的构造   总被引:1,自引:0,他引:1  
S-box是密码理论与实践中十分重要的一种装置 ,它的密码性能由其分量函数所决定 .于是 ,选择适当的分量函数来构造 S-box就成了一个重要的研究课题 .在一定意义上 ,Bent函数是最优良的密码函数 .本文通过函数序列半群和置换群来构造其任何非零线性组合为 Bent函数与线性函数之和的函数组 ,从而可由 Bent函数构造出具有高度非线性度和其他良好性状的 S-box  相似文献   
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TheExistenceofPeriodicOrbitsforHigherDimensionalAutonomousSystemswithSmallPerturbationsJiangLiqing(蒋里强);ZhouYi(周毅);FanYe(范晔)(...  相似文献   
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极值图论与度序列   总被引:4,自引:0,他引:4  
李炯生  尹建华 《数学进展》2004,33(3):273-283
本文简要概述极值图论与度序列的最新研究进展,同时提出了一些有待进一步解决的问题和猜想.  相似文献   
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