Light edges in 1-planar graphs with prescribed minimum degree

• Autorzy: Dávid Hudák , Peter Šugerek
• Języki publikacji: EN

Abstrakty

EN

A graph is called 1-planar if it can be drawn 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 δ ≥ 4 contains an edge with degrees of its endvertices of type (4, ≤ 13) or (5, ≤ 9) or (6, ≤ 8) or (7,7). We also show that for δ ≥ 5 these bounds are best possible and that the list of edges is minimal (in the sense that, for each of the considered edge types there are 1-planar graphs whose set of types of edges contains just the selected edge type).

Słowa kluczowe

EN

light edge; 1-planar graph

Kategorie tematyczne

• 05C10: Planar graphs; geometric and topological aspects of graph theory

• Wydawca: De Gruyter Open
• Czasopismo: Discussiones Mathematicae Graph Theory
• Rocznik: 2012
• Tom: 32
• Numer: 3
• Strony: 545-556

Daty

wydano

2012

otrzymano

2011-03-03

poprawiono

2011-09-29

zaakceptowano

2011-09-29

Twórcy

autor

Dávid Hudák

• Institute of Mathematics, Faculty of Science, Pavol Jozef Šafárik University, Jesenná 5, 040 01 Košice, Slovakia

autor

Peter Šugerek

• Institute of Mathematics, Faculty of Science, Pavol Jozef Šafárik University, Jesenná 5, 040 01 Košice, Slovakia

Bibliografia

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Identyfikatory

DOI

10.7151/dmgt.1625