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  • Planar graph  (1)
  • Primary: 06A10  (1)
  • 1
    Electronic Resource
    Electronic Resource
    Every triangle-free planar graph has a planar upward drawing (1993)
    Springer
    Order 10 (1993), S. 1-16 
    Details
    ISSN: 1572-9273
    Keywords: 06A06 ; Planar graph ; triangle-free ; upward drawing
    Source: Springer Online Journal Archives 1860-2000
    Topics: Mathematics
    Notes: Abstract A planar ordered set has a triangle-free, planar covering graph; on the other hand, there are nonplanar ordered sets whose covering graphs are planar. We show thatevery triangle-free planar graph has a planar upward drawing. This planar upward drawing can be constructed in time, polynomial in the number of vertices. Our results shed light on the apparently difficult problem, of long-standing, whether there is aneffective planarity-testing procedure for an ordered set.
    Type of Medium: Electronic Resource
    URL: http://dx.doi.org/10.1007/BF01108704
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  • 2
    Electronic Resource
    Electronic Resource
    Constructing greedy linear extensions by interchanging chains (1986)
    Springer
    Order 3 (1986), S. 107-121 
    Details
    ISSN: 1572-9273
    Keywords: Primary: 06A10 ; secondary: 68C25 ; Linear extension ; greedy ; chain interchange ; subdiagram
    Source: Springer Online Journal Archives 1860-2000
    Topics: Mathematics
    Notes: Abstract A natural way to prove that a particular linear extension of an ordered set is ‘optimal’ with respect to the ‘jump number’ is to transform this linear extension ‘canonically’ into one that is ‘optimal’. We treat a ‘greedy chain interchange’ transformation which has applications to ordered sets for which each ‘greedy’ linear extension is ‘optimal’.
    Type of Medium: Electronic Resource
    URL: http://dx.doi.org/10.1007/BF00390102
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