期刊论文

Song, Fei-fei

英文

应用数学学报：英文版

0168-9673

2019

35

4

919-923

10.1007/s10255-019-0864-0

05C05 05C07 publisher-imprint-name Institute of Applied Mathematics, Chinese Academy of Sciences and Chinese Mathematical Society, co-publsihed with Springer volume-issue-count 4 issue-article-count 20 issue-toc-levels 0 issue-pricelist-year 2019 issue-copyright-holder Institute of Applied Mathematics, Academy of Mathematics and System Sciences, Chinese Academy of Sciences and Springer-Verlag GmbH Germany, part of Springer Nature issue-copyright-year 2019 article-contains-esm No article-numbering-style Unnumbered article-registration-date-year 2019 article-registration-date-month 12 article-registration-date-day 18 article-toc-levels 0 toc-levels 0 volume-type Regular journal-product ArchiveJournal numbering-style Unnumbered article-grants-type Regular metadata-grant OpenAccess abstract-grant OpenAccess bodypdf-grant Restricted bodyhtml-grant Restricted bibliography-grant Restricted esm-grant OpenAccess online-first false pdf-file-reference BodyRef/PDF/10255_2019_Article_864.pdf target-type OnlinePDF issue-online-date-year 2019 issue-online-date-month 12 issue-online-date-day 19 issue-type Regular article-type OriginalPaper journal-subject-primary Mathematics journal-subject-secondary Applications of Mathematics journal-subject-secondary Math Applications in Computer Science journal-subject-secondary Theoretical, Mathematical and Computational Physics journal-subject-collection Mathematics and Statistics open-access false Partially supported by National Natural Science Foundation of China (No. 11771172), key scientific and technological project of higher education of Henan Province (No. 19A110019) and Science and technology innovation fund of Henan Agricultural University (No. KJCX2019A15). Partially supported by the PhD Research Foundation of Henan Agricultural University (No. 30500614).

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A k-tree is a tree with maximum degree at most k. In this paper, we give a sharp degree sum condition for a graph to have a spanning k-tree in which specified vertices have degree less than t, where 1 ≤ t ≤ k. We denote by σk(G) the minimum value of the degree sum of k independent vertices in a graph G. Let k ≥ 2, s ≥ 0 and 1 ≤ t ≤ k be integers, and suppose G is an (s + 1)-connected graph with σk(G) ≥∣G∣ + (k − t)s − 1. Then for any s specified vertices, G contains a spanning k-tree in which every specified vertex has degree at mo...