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  • 1 University of Pannonia Department of Computer Science and Systems Technology Egyetem u. 10 8200 Veszprém Hungary
  • 2 University of Szeged Bolyai Institute Aradi vértanúk tere 1 6720 Szeged Hungary
  • 3 Zhengzhou University Department of Mathematics Zhengzhou, Henan 450052 China
  • 4 Hefei University of Technology School of Management Hefei 230009 China
  • 5 Monash University School of Mathematical Sciences Victoria 3800 Australia
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Kinnersley and Langston used a computer search to characterize the class of graphs with path-width at most two. The excluded minor list consists of 110 graphs. This set is fairly large, and the list gives little insight to structural properties of the targeted graph class. We take a different route here. We concentrate on the building blocks of the graphs with path-width at most two and how they are glued together. In this way, we get a short and compact characterization of 2-connected and 2-edge-connected graphs with path-width at most two.

  • Barát, J., Width-type graph parameters, PhD thesis, University of Szeged, (2001), 90 pages.

  • Barát, J. and Hajnal, P., Operations which preserve path-width at most two, Comb. Probab. Comput., 10 (2001), 277–291. MR 1860436 (2002g: 05171)

    Hajnal P. , 'Operations which preserve path-width at most two ' (2001 ) 10 Comb. Probab. Comput. : 277 -291.

    • Search Google Scholar
  • Barát, J. and Hajnal, P., Partial tracks; characterizatons and recognition of graphs with path-width at most two. http://www.math.u-szeged.hu/~barat/bjhp_siam.pdf

  • Bienstock, D., Robertson, N., Seymour, P. and Thomas, R., Quickly Excluding a Forest, J. Comb. Theory Ser. B, 52 (1991), no. 2, 274–283. MR 1110475 (92f:05034)

    Thomas R. , 'Quickly Excluding a Forest ' (1991 ) 52 J. Comb. Theory Ser. B : 274 -283.

  • Bondy, A. and Murty, U. S. R., Graph Theory, Graduate Texts in Mathematics, 244. Springer, New York, (2008) xii + 651 pp. MR 2368647 (2009c:05001)

    Murty U. S. R. , '', in Graduate Texts in Mathematics , (2008 ) -.

  • Bodlaender, H. L. and de Fluiter, B., Intervalizing k-colored graphs, Technical report UU-CS-1995-15, 153 pages. MR 1466460. (English summary) Automata, languages and programming (Szeged, 1995), 87–98, Lecture Notes in Comput. Sci., 944, Springer, Berlin, 1995.

  • Bodlaender, H. L. and de Fluiter, B., On intervalizing k-colored graphs for DNA physical mapping, Discrete Appl. Math., 71 (1996), no. 1–3, 55–77. MR 1420292 (98d:92008)

    Fluiter B. , 'On intervalizing k-colored graphs for DNA physical mapping ' (1996 ) 71 Discrete Appl. Math. : 55 -77.

    • Search Google Scholar
  • Diestel, R., Graph Minors I: a short proof of the path width theorem, Comb. Probab. Comput., 4 (1995), 27–30. MR 1336653 (96b:05077). Comment on: “Graph minors. I. Excluding a forest” [J. Combin. Theory Ser. B, 35 (1983), no. 1, 39–61; MR 0723569 (85d:05148)] by N. Robertson and P. D. Seymour (English summary).

    Diestel R. , 'Graph Minors I: a short proof of the path width theorem ' (1995 ) 4 Comb. Probab. Comput. : 27 -30.

    • Search Google Scholar
  • Gupta, A., Nishimura, N., Proskurowski, A. and Ragde, P., Embeddings of k-connected graphs of pathwidth k, Discrete Appl. Math., 145 (2005), no. 2, 242–265. MR 2113145 (2005i:05044)

    Ragde P. , 'Embeddings of k-connected graphs of pathwidth k ' (2005 ) 145 Discrete Appl. Math. : 242 -265.

    • Search Google Scholar
  • Kinnersley, N. G., The vertex separation number of a graph equals its path-width, Inf. Proc. Letters, 42 (1992), no. 6, 345–350. MR 1178214 (93d:05143)

    Kinnersley N. G. , 'The vertex separation number of a graph equals its path-width ' (1992 ) 42 Inf. Proc. Letters : 345 -350.

    • Search Google Scholar
  • Kinnersley, N. G. and Langston, M. A., Obstruction set isolation for the gate matrix layout problem, Discrete Appl. Math., 54 (1994), 169–213. MR 1300245 (95h:68089)

    Langston M. A. , 'Obstruction set isolation for the gate matrix layout problem ' (1994 ) 54 Discrete Appl. Math. : 169 -213.

    • Search Google Scholar
  • Lin, Y. and Yang, A., The Series Structure Characterization of Graphs with Path-width at Most Two, http://www.math.u-szeged.hu/~barat/lin_yang.pdf

  • Möhring, R. H., Graph problem related to gate matrix layout and PLA folding, Computing Suppl., 7 (1990), 17–51. MR 1059923

    Möhring R. H. , 'Graph problem related to gate matrix layout and PLA folding ' (1990 ) 7 Computing Suppl. : 17 -51.

    • Search Google Scholar
  • Nash-Williams, C. St. J. A., On well-quasi-ordering trees, Theory of Graphs and its Applications (Proc. Sympos. Smolenice, 1963) (1964), 83–84. MR 0173252 (30#3465)

  • Robertson, N. and Seymour, P. D., Graph Minors I. Excluding a forest, J. Comb. Theory Ser. B., 35 (1983), 39–61. MR 0723569 (85d:05148)

    Seymour P. D. , 'Graph Minors I. Excluding a forest ' (1983 ) 35 J. Comb. Theory Ser. B. : 39 -61.

    • Search Google Scholar
  • Robertson, N. and Seymour, P. D., Graph Minors IV. Tree-width and well-quasiordering, J. Comb. Theory Ser. B., 48 (1990), 227–254. MR 1046757 (91g:05039)

    Seymour P. D. , 'Graph Minors IV. Tree-width and well-quasiordering ' (1990 ) 48 J. Comb. Theory Ser. B. : 227 -254.

    • Search Google Scholar
  • Robertson, N. and Seymour, P. D., Graph Minors V. Excluding a planar graph, J. Comb. Theory Ser. B., 41 (1986), no. 1, 92–114. MR 0854606 (89m:05070)

    Graph Minors V. , 'Excluding a planar graph ' (1986 ) 41 J. Comb. Theory Ser. B. : 92 -114.

  • Takahashi, A., Ueno, S. and Kajitani, Y., Minimal acyclic forbidden minors for the family of graphs with bounded path-width, Discrete Math., 127 (1994), 293–304. MR 1273610 (96d:05074)

    Kajitani Y. , 'Minimal acyclic forbidden minors for the family of graphs with bounded path-width ' (1994 ) 127 Discrete Math. : 293 -304.

    • Search Google Scholar
  • Thomas, R., Tree-decomposition of graphs, Class Notes (1996). http://www.math.gatech.edu/~thomas/tree.ps

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  • Biró, András (Number theory)
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