On local structure of 1-planar graphs of minimum degree 5 and girth 4

نویسندگان

  • Dávid Hudák
  • Tomás Madaras
چکیده

A graph is 1-planar if it can be embedded in the plane so that each edge is crossed by at most one other edge. We prove that each 1-planar graph of minimum degree 5 and girth 4 contains (1) a 5-vertex adjacent to an ≤ 6-vertex, (2) a 4-cycle whose every vertex has degree at most 9, (3) a K1,4 with all vertices having degree at most 11.

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عنوان ژورنال:
  • Discussiones Mathematicae Graph Theory

دوره 29  شماره 

صفحات  -

تاریخ انتشار 2009