共查询到20条相似文献,搜索用时 31 毫秒
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In this paper, we give the dimension and the minimum distance of two subclasses of narrow-sense primitive BCH codes over with designed distance for all , where q is a prime power and is a positive integer. As a consequence, we obtain an affirmative answer to two conjectures proposed by C. Ding in 2015. Furthermore, using the previous part, we extend some results of Yue and Hu [16], and we give the dimension and, in some cases, the Bose distance for a large designed distance in the range for , where if m is odd, and if m is even. 相似文献
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《Discrete Mathematics》2023,346(4):113304
In 1965 Erd?s asked, what is the largest size of a family of k-element subsets of an n-element set that does not contain a matching of size ? In this note, we improve upon a recent result of Frankl and resolve this problem for and . 相似文献
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In this paper, we study a multiple-terminal extension of the classic Hamiltonian path problem where salesmen are initially located at different depots and finally stopped at different terminals. To the best of our knowledge, only 2-approximation algorithm is available in the literature. For arbitrary , we first present a Christofides-like heuristic with a tight approximation ratio of . Besides, we also develop a -approximation algorithm by divide-and-conquer technique. The -approximation algorithm runs in polynomial time for fixed and . 相似文献
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《Discrete Mathematics》2022,345(11):113029
Let G be a k-connected graph on n vertices. Hippchen's Conjecture (2008) states that two longest paths in G share at least k vertices. Gutiérrez (2020) recently proved the conjecture when or . We improve upon both results; namely, we show that two longest paths in G share at least k vertices when or . This completely resolves two conjectures by Gutiérrez in the affirmative. 相似文献
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《Discrete Mathematics》2022,345(12):113082
Let G be a graph of order n with an edge-coloring c, and let denote the minimum color-degree of G. A subgraph F of G is called rainbow if all edges of F have pairwise distinct colors. There have been a lot of results on rainbow cycles of edge-colored graphs. In this paper, we show that (i) if , then every vertex of G is contained in a rainbow triangle; (ii) if and , then every vertex of G is contained in a rainbow ; (iii) if G is complete, and , then G contains a rainbow cycle of length at least k, where . 相似文献
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《Discrete Mathematics》2022,345(3):112731
Let be the matching number of a graph G. A characterization of the graphs with given maximum odd degree and smallest possible matching number is given by Henning and Shozi (2021) [13]. In this paper we complete our study by giving a characterization of the graphs with given maximum even degree and smallest possible matching number. In 2018 Henning and Yeo [10] proved that if G is a connected graph of order n, size m and maximum degree k where is even, then , unless G is k-regular and . In this paper, we give a complete characterization of the graphs that achieve equality in this bound when the maximum degree k is even, thereby completing our study of graphs with given maximum degree and smallest possible matching number. 相似文献
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Let M be a random rank-r matrix over the binary field , and let be its Hamming weight, that is, the number of nonzero entries of M.We prove that, as with r fixed and tending to a constant, we have that converges in distribution to a standard normal random variable. 相似文献
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We construct a class of -additive cyclic codes generated by pairs of polynomials, where p is a prime number. Based on probabilistic arguments, we determine the asymptotic rates and relative distances of this class of codes: the asymptotic Gilbert-Varshamov bound at is greater than and the relative distance of the code is convergent to δ, while the rate is convergent to for and . As a consequence, we prove that there exist numerous asymptotically good -additive cyclic codes. 相似文献
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《Discrete Mathematics》2023,346(4):113288
Square coloring is a variant of graph coloring where vertices within distance two must receive different colors. When considering planar graphs, the most famous conjecture (Wegner, 1977) states that colors are sufficient to square color every planar graph of maximum degree Δ. This conjecture has been proven asymptotically for graphs with large maximum degree. We consider here planar graphs with small maximum degree and show that colors are sufficient, which improves the best known bounds when . 相似文献
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