IJPAM: Volume 67, No. 1 (2011)

A NOTE ON UPPER BOUND FOR -COVERED
TRIANGULATION OF CLOSED SURFACES

Ashish K. UpadhyayDepartment of Mathematics, Indian Institute of Technology Patna, Patliputra Colony, Patna, 800013, INDIA
School of Basic and Applied Sciences
Guru Gobind Singh Indraprastha University
Kashmere Gate, Delhi, 110006, INDIA

Abstract.A triangulation of a closed surface is said to be -covered if at least one vertex in each edge has degree . In [#!NeNa!#] the authors have shown that: (a) if a closed surface of non-positive Euler characteristic admits a -covered triangulation then , and (b) the upper bound for is attained when: and for , whenever is a positive integer. In this note we show that the upper bound is attained for .