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New Classes of Extremal Graphs with Given Bandwidth

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Abstract

The bandwidth is an important invariant in both theoretic and applied fields. The extremal graph problem on bandwidth is to determine the minimum size of a graph G with order n and bandwidth B, denoted by m(n, B). The results of m(n, n − 1) and m(n, n − 2) have been known in the literature. This paper studies m(n, n − 3) as well as the extremal graphs. In particular, we concentrate on a relation between m(n, n − 3) and ex(n, C 4), i.e., the maximum size of a graph without 4-cycles. The latter is a well-known open problem proposed by P. Erdös more than 70 years ago.

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Authors and Affiliations

  1. The Key Laboratory of Embedded System and Service Computing, Ministry of Education, Tongji University, Shanghai, 200092, China

    Lan Lin

  2. School of Electronics and Information Engineering, Tongji University, Shanghai, 200092, China

    Lan Lin

  3. Department of Mathematics, Zhengzhou University, Zhengzhou, 450001, China

    Yixun Lin

Authors
  1. Lan Lin
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  2. Yixun Lin
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Correspondence to Yixun Lin.

Additional information

Supported by NSFC (11101383, 61373106), 973 Program of China (2010CB328101).

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Lin, L., Lin, Y. New Classes of Extremal Graphs with Given Bandwidth. Graphs and Combinatorics 31, 149–167 (2015). https://doi.org/10.1007/s00373-013-1386-9

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  • DOI: https://doi.org/10.1007/s00373-013-1386-9

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