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Looseness and Independence Number of Triangulations on Closed Surfaces

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Nakamoto A., Negami S., Ohba K., Suzuki Y.

Discussiones Mathematicae Graph Theory

2016

tom 36

nr 3

545-554

The looseness of a triangulation G on a closed surface F2, denoted by ξ (G), is defined as the minimum number k such that for any surjection c : V (G) → {1, 2, . . . , k + 3}, there is a face uvw of G with c(u), c(v) and c(w) all distinct. We shall bound ξ (G) for triangulations G on closed surfaces by the independence number of G denoted by α(G). In particular, for a triangulation G on the sphere, we have [...] and this bound is sharp. For a triangulation G on a non-spherical surface F2, we have ξ (G) ≤ 2α(G) + l(F2) − 2, where l(F2) = [(2 − χ(F2))/2] with Euler characteristic χ(F2).

Ograniczanie wyników

1 Discussiones Mathematicae Graph Theory

1 Nakamoto A.

1 Negami S.

1 Ohba K.

1 Suzuki Y.

1 2016

Wyniki wyszukiwania

Looseness and Independence Number of Triangulations on Closed Surfaces