19-25 June 2011
Bled, Slovenia
Europe/Ljubljana timezone
Home > Timetable > Contribution details
PDF | XML

Light edges in 1-planar graphs with prescribed minimum degree

Presented by Mr. Peter ŠUGEREK
Type: Oral presentation
Track: Crossing Number

Content

According to the famous theorem of A. Kotzig on light edges in 3-connected planar graphs we investigate light edges in certain nonplanar graphs which can be drawn in the plane in such a way that each edge is crossed by at most one other edge; such graphs are called 1-planar. We prove that each 1-planar graph of minimum degree δ≥4 contains an edge with degrees its endvertices of type (4, ≥13) or (5, ≥9) or (6, ≥8) or (7,7). We also show that for δ≥5 are these bounds best possible and that the list of edge types is minimal. Key words: 1-planar graph, light edge

Place

Location: Bled, Slovenia
Address: Best Western Hotel Kompas Bled

Primary authors

More