Abstract
The cutwidth problem for a graph G is to embed G into a path such that the maximum number of overlap edges (i.e., the congestion) is minimized. The investigations of critical graphs and their structures are meaningful in the study of a graph-theoretic parameters. We study the structures of k-cutwidth \((k>1)\) critical trees, and use them to characterize the set of all 4-cutwidth critical trees.
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References
Bondy JA, Murty USR (2008) Graph theory. Springer, New York
Chung FRK, Seymour PD (1985) Graphs with small bandwidth and cutwidth. Discret Math 75:268–277
Chung MJ, Makedon F, Sudborough IH, Turner J (1985) Polynomial time algorithms for the min cut problem on degree restricted trees. SIAM J Comput 14:158–177
Diaz J, Petit J, Serna M (2002) A survey of graph layout problems. ACM Comput Surv 34:313–356
Garey MR, Johnson DS (1979) Computers and intractability: a guide to the theory of NP-completeness. W. H. Freeman & Company, San Francisco
Korach E, Solel N (1993) Treewidth, pathwidth and cutwidth. Discret Appl Math 43:97–101
Lin Y, Yang A (2004) On 3-cutwidth critical graphs. Discret Math 275:339–346
Lin Y, Li X, Yang A (2002) A degree sequence method for the cutwidth problem of graphs. Appl Math J Chin Univ B 17(2):125–134
Lin Y (2003) The cutwidth of trees with diameter at most 4. Appl Math J Chin Univ B 18(3):361–369
Liu H, Yuan J (1995) Cutwidth problem on graphs. Appl Math J Chin Univ A 10(3):339–348
Rolin J, Sykora O, Vrto I (1995) Optimal cutwidth of meshes., Lecture Notes in Computer Science. Springer, Berlin
Yannakakis M (1985) A polynomial algorithm for the min-cut arrangement of trees. J ACM 32:950–989
Zhang Z, Lin Y (2012) On 4-cutwidth critical trees. ARS Comb 105:149–160
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Zhang, ZK., Lai, HJ. Characterizations of k-cutwidth critical trees. J Comb Optim 34, 233–244 (2017). https://doi.org/10.1007/s10878-016-0061-5
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DOI: https://doi.org/10.1007/s10878-016-0061-5