On local structure of 1-planar graphs of minimum degree 5 and girth 4
Dávid Hudák ; Tomás Madaras
Discussiones Mathematicae Graph Theory, Tome 29 (2009), p. 385-400 / Harvested from The Polish Digital Mathematics Library
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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.

Publié le : 2009-01-01
EUDML-ID : urn:eudml:doc:270802 
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Dávid Hudák; Tomás Madaras. On local structure of 1-planar graphs of minimum degree 5 and girth 4. Discussiones Mathematicae Graph Theory, Tome 29 (2009) pp. 385-400. http://gdmltest.u-ga.fr/item/bwmeta1.element.bwnjournal-article-doi-10_7151_dmgt_1454/

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