Crossing-Critical Graphs and Path-Width

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Crossing-Critical Graphs and Path-Width (2001) (Make Corrections) (1 citation)
Petr HlinenyGraph Drawing

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Abstract: . The crossing number cr(G) of a graph G, is the smallest possible number of edge-crossings in a drawing of G in the plane. A graph G is crossing-critical if cr(G e) < cr(G) for all edges e of G. G. Salazar conjectured in 1999 that crossing-critical graphs have pathwidth bounded by a function of their crossing number, which roughly means that such graphs are made up of small pieces joined in a linear way on small cut-sets. That conjecture was recently proved by the author [9]. Our paper... (Update)

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BibTeX entry: (Update)

P. Hlineny. Crossing critical graphs and path-width. In Proc. 9th Intl. Symposium on Graph Drawing, volume 2265 of Lecture Notes in Computer Science, pages 102-114, Springer Verlag, 2001. http://citeseer.ist.psu.edu/hlineny01crossingcritical.html More

@inproceedings{ hlineny01crossingcritical,
    author = "Petr Hlineny",
    title = "Crossing-Critical Graphs and Path-Width",
    booktitle = "Graph Drawing",
    pages = "102-114",
    year = "2001",
    url = "citeseer.ist.psu.edu/hlineny01crossingcritical.html" }

Citations (may not include all citations):
131 Graph Drawing: Algorithms for the Visualization of Graphs (context) - Di Battista, Eades et al. - 1999
113 Crossing number is NP-complete (context) - Garey, Johnson - 1983
64 Complexity Issues in VLSI (context) - Leighton - 1983
38 Excluding a forest (context) - Robertson, Seymour et al. - 1983
20 Quickly excluding a forest (context) - Bienstock, Robertson et al. - 1991
16 Toward a theory of crossing numbers (context) - Tutte
14 Intersections of curve systems and the crossing number of C5.. (context) - Richter, Thomassen - 1995
4 Construction of crossing-critical graphs (context) - Kochol - 1987
2 The crossing number of C6Cn (context) - Richter, Salazar - 2001
2 Embedding grids on surfaces (context) - Geelen, Richter et al.
2 Large four-connected nonplanar graphs (context) - Ding, Oporowski et al.
2 A frame for solving VLSI graph layout problems (context) - Bhatt, Leighton - 1984
2 Crossing-number critical graphs have bounded path-width (context) - Hlin
2 North-Holland Math (context) - Ajtai, Chv et al. - 1982
1 is true for all but nitely n (context) - Glebsky, Salazar et al.

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