Abstract
Let m, n, r and \(k_i\) \((1\le i\le m)\) be positive integers with \(n\le m\) and \(k_1\ge k_2\ge \cdots \ge k_m\ge 2r-1\). Let G be a graph, and let \(H_1,H_2,\cdots ,H_r\) be vertex-disjoint n-subgraphs of G. It is verified in this article that every \([0,k_1+k_2+\cdots +k_m-n+1]\)-graph G includes a subgraph R such that R has a \([0,k_i]_1^{n}\)-factorization orthogonal to every \(H_i\), \(1\le i\le r\).
Supported by the National Natural Science Foundation of China (Grant No. 11371009), the National Social Science Foundation of China (Grant No. 14AGL001) and the Natural Science Foundation of the Higher Education Institutions of Jiangsu Province (Grant No. 14KJD110002), and sponsored by 333 Project of Jiangsu Province.
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The authors are grateful to the anonymous referees for their very helpful and detailed comments in improving this paper.
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Zhou, S., Zhang, T., Xu, Z. (2017). Subgraphs with Orthogonal \([0,k_{i}]_{1}^{n}\)-Factorizations in Graphs. In: Gaur, D., Narayanaswamy, N. (eds) Algorithms and Discrete Applied Mathematics. CALDAM 2017. Lecture Notes in Computer Science(), vol 10156. Springer, Cham. https://doi.org/10.1007/978-3-319-53007-9_32
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DOI: https://doi.org/10.1007/978-3-319-53007-9_32
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