Hostname: page-component-76fb5796d-vvkck Total loading time: 0 Render date: 2024-04-26T07:40:15.143Z Has data issue: false hasContentIssue false
  • English
  • Français

Cutwidth of iterated caterpillars∗

Published online by Cambridge University Press:  11 March 2013

Lan Lin  and
Yixun Lin
Lan Lin
Affiliation:
School of Electronics and Information Engineering, Tongji University, Shanghai 200092, China. The Key Laboratory of Embedded System and Service Computing, Ministry of Education, Tongji University, Shanghai 200092, China
Yixun Lin
Affiliation:
Department of Mathematics, Zhengzhou University, Zhengzhou 450052, China. linyixun@zzu.edu.cn
Get access

Abstract

The cutwidth is an important graph-invariant in circuit layout designs. The cutwidth of a graph G is the minimum value of the maximum number of overlap edges when G is embedded into a line. A caterpillar is a tree which yields a path when all its leaves are removed. An iterated caterpillar is a tree which yields a caterpillar when all its leaves are removed. In this paper we present an exact formula for the cutwidth of the iterated caterpillars.

Keywords

Circuit layout designgraph labelingcutwidthcaterpillariterated caterpillar
Type
Research Article
Information
RAIRO - Theoretical Informatics and Applications , Volume 47 , Issue 2 , April 2013 , pp. 181 - 193
Copyright
© EDP Sciences 2013

Access options

Get access to the full version of this content by using one of the access options below. (Log in options will check for institutional or personal access. Content may require purchase if you do not have access.)

References

J.A. Bondy and U.S.R. Murty, Graph Theory. Springer-Verlag, Berlin (2008).
F.R.K. Chung, Labelings of graphs, edited by L.W. Beineke and R.J. Wilson. Selected Topics in Graph Theory 3 (1988) 151–168.
Chung, F.R.K., On the cutwidth and topological bandwidth of a tree. SIAM J. Algbr. Discrete Methods 6 (1985) 268–277. Google Scholar
Diaz, J., Petit, J. and Serna, M., A survey of graph layout problems. ACM Comput. Surveys 34 (2002) 313–356. Google Scholar
Gallian, J.A., A survey: recent results, conjectures, and open problems in labeling graphs. J. Graph Theory 13 (1989) 491–504. Google Scholar
M.R. Garey and D.S. Johnson, Computers and Intractability: A Guide to the Theory of NP-Completeness. W.H. Freeman, San Francisco (1979).
Lengauer, T., Upper and lower bounds for the min-cut linear arrangement of trees. SIAM J. Algbr. Discrete Methods 3 (1982) 99–113. Google Scholar
Lin, Y., Li, X. and Yang, A., A degree sequence method for the cutwidth problem of graphs. Appl. Math. J. Chinese Univ. Ser. B 17(2) (2002) 125–134. Google Scholar
Lin, Y., The cutwidth of trees with diameter at most 4. Appl. Math. J. Chinese Univ. Ser. B 18(3) (2003) 361–368. Google Scholar
Liu, H. and Yuan, J., The cutwidth problem for graphs. Appl. Math. J. Chinese Univ. Ser. A 10 (3) (1995) 339–348. Google Scholar
Monien, B., The bandwidth minimization problem for caterpipals with hair length 3 is NP-complete. SIAM J. Algbr. Discrete Methods 7 (1986) 505–512. Google Scholar
Rolin, J., Sykora, O. and Vrt’o, I., Optimal cutwidths and bisection widths of 2- and 3-dimensional meshes. Lect. Notes Comput. Sci. 1017 (1995) 252–264. Google Scholar
Syslo, M. M. and Zak, J., The bandwidth problem: critical subgraphs and the solution for caterpillars. Annal. Discrete Math. 16 (1982) 281–286. Google Scholar
Vrt'o, I., Cutwidth of the r-dimensional mesh of d-ary trees. RAIRO Theor. Inform. Appl. 34 (2000) 515–519. Google Scholar
Yanakakis, M., A polynomial algorithm for the min-cut arrangement of trees. J. ACM 32 (1985) 950–989. Google Scholar