On Light Edges and Triangles in Planar Graphs of Minimum Degree Five | Zendy

Borodin Oleg V. | Zendy; Sanders Daniel P. | Zendy

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On Light Edges and Triangles in Planar Graphs of Minimum Degree Five

Author(s) -

Borodin Oleg V.,

Sanders Daniel P.

Publication year - 1994

Publication title -

mathematische nachrichten

Language(s) - English

Resource type - Journals

SCImago Journal Rank - 0.913

H-Index - 50

eISSN - 1522-2616

pISSN - 0025-584X

DOI - 10.1002/mana.19941700103

Subject(s) - mathematics , planar graph , combinatorics , outerplanar graph , planar , graph , 1 planar graph , degree (music) , polyhedral graph , discrete mathematics , pathwidth , line graph , computer science , physics , computer graphics (images) , acoustics

This paper presents two tight inequalities for planar graphs of minimum degree five. An edge or face of a plane graph is light if the sum of the degrees of the vertices incident with it is small. A light edge inequality is presented which shows that planar graphs of minimum degree five have a large number of light edges; a graph is presented which shows that this inequality cannot be improved. This completes work contributed to by Wernicke , Grünbaum , Fisk , and Borodin . A graph is presented which shows that a similar light triangle inequality of Borodin is best possible; no such graph had been previously found.

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