On Gallai's conjecture for series-parallel graphs and planar 3-trees

نویسندگان

  • Philipp Kindermann
  • Lena Schlipf
  • André Schulz
چکیده

A path cover is a decomposition of the edges of a graph into edge-disjoint simple paths. Gallai conjectured that every connected n-vertex graph has a path cover with at most dn/2e paths. We prove Gallai’s conjecture for series-parallel graphs. For the class of planar 3-trees we show how to construct a path cover with at most b5n/8c paths, which is an improvement over the best previously known bound of b2n/3c.

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عنوان ژورنال:
  • CoRR

دوره abs/1706.04130  شماره 

صفحات  -

تاریخ انتشار 2017