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

• Autorzy: Dávid Hudák , Tomás Madaras
• Języki publikacji: EN

Abstrakty

EN

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 $K_{1,4}$ with all vertices having degree at most 11.

Słowa kluczowe

EN

light graph; 1-planar graph; star; cycle

Kategorie tematyczne

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

• Wydawca: De Gruyter Open
• Czasopismo: Discussiones Mathematicae Graph Theory
• Rocznik: 2009
• Tom: 29
• Numer: 2
• Strony: 385-400

Daty

wydano

2009

otrzymano

2007-11-13

poprawiono

2008-07-28

zaakceptowano

2008-07-28

Twórcy

autor

Dávid Hudák

• Institute of Mathematics, Faculty of Sciences, University of P. J. Šafárik, Jesenná 5, 040 01 Košice, Slovak Republic

autor

Tomás Madaras

• Institute of Mathematics, Faculty of Sciences, University of P. J. Šafárik, Jesenná 5, 040 01 Košice, Slovak Republic

Bibliografia

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• [9] S. Jendrol', T. Madaras, R. Soták and Z. Tuza, On light cycles in plane triangulations, Discrete Math. 197/198 (1999) 453-467, doi: 10.1016/S0012-365X(99)90099-7.
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• [11] G. Ringel, Ein Sechsfarbenproblem auf der Kügel, Abh. Math. Sem. Univ. Hamburg 29 (1965) 107-117, doi: 10.1007/BF02996313.
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Identyfikatory

DOI

10.7151/dmgt.1454