Minimal acyclic forbidden minors for the family of graphs with bounded path-width

The graphs with bounded path-width, introduced by Robertson and Seymour, and the graphs with bounded proper-path-width, introduced in this paper, are investigated. These families of graphs are minor-closed. We characterize the minimal acyclic forbidden minors for these families of graphs. We also give estimates for the numbers of minimal forbidden minors and for the numbers of vertices of the largest minimal forbidden minors for these families of graphs.

[1]  Stefan Arnborg,et al.  Forbidden minors characterization of partial 3-trees , 1990, Discret. Math..

[2]  Atsushi Takahashi,et al.  Mixed Searching and Proper-Path-Width , 1991, Theor. Comput. Sci..

[3]  Michael R. Fellows,et al.  On search decision and the efficiency of polynomial-time algorithms , 1989, STOC '89.

[4]  Michael A. Langston,et al.  Finite-Basis Theorems and a Computation-Integrated Approach to Obstruction Set Isolation , 1989, Computers and Mathematics.

[5]  Derek G. Corneil,et al.  Complexity of finding embeddings in a k -tree , 1987 .

[6]  K. Wagner.  Bemerkungen zu Hadwigers Vermutung , 1960 .

[7]  Dan Archdeacon,et al.  A Kuratowski theorem for the projective plane , 1981, J. Graph Theory.

[8]  Atsushi Takahashi,et al.  Universal Graphs for Graphs with Bounded Path-Width , 1995 .

[9]  P. Scheffler,et al.  A Linear Algorithm for the Pathwidth of Trees , 1990 .

[10]  Paul D. Seymour,et al.  Graph minors. I. Excluding a forest , 1983, J. Comb. Theory, Ser. B.

[11]  W.W.-M. Dai,et al.  Minimal forbidden minor characterization of planar partial 3-trees and application to circuit layout , 1990, IEEE International Symposium on Circuits and Systems.

[12]  T. D. Parsons,et al.  Embeddings of bipartite graphs , 1983, J. Graph Theory.

[13]  T. D. Parsons,et al.  Pursuit-evasion in a graph , 1978 .

[14]  Rolf H. Möhring,et al.  Graph Problems Related to Gate Matrix Layout and PLA Folding , 1990 .

[15]  Andrzej Proskurowski,et al.  Separating subgraphs in k-trees: Cables and caterpillars , 1984, Discret. Math..

[16]  Atsushi Takahashi,et al.  On the Proper-Path-Decomposition of Trees , 1995 .

[17]  Henry H. Glover,et al.  103 Graphs that are irreducible for the projective plane , 1979, J. Comb. Theory, Ser. B.