Looseness and Independence Number of Triangulations on Closed Surfaces
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...
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2016-08-01
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| Series: | Discussiones Mathematicae Graph Theory |
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| Online Access: | https://doi.org/10.7151/dmgt.1870 |
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doaj-3c94ed50f05a477b88adf2c8852faa392021-09-05T17:20:21ZengSciendoDiscussiones Mathematicae Graph Theory2083-58922016-08-0136354555410.7151/dmgt.1870dmgt.1870Looseness and Independence Number of Triangulations on Closed SurfacesNakamoto Atsuhiro0Negami Seiya1Ohba Kyoji2Suzuki Yusuke3Graduate School of Environment and Information Science Yokohama National University 79-7 Tokiwadai, Hodogaya-Ku, Yokohama 240-8501, JapanGraduate School of Environment and Information Science Yokohama National University 79-7 Tokiwadai, Hodogaya-Ku, Yokohama 240-8501, JapanYonago National College of Technology Yonago, Tottori 683-8502, JapanDepartment of Mathematics Niigata University 8050 Ikarashi 2-no-cho, Nishi-ku, Niigata, 950-2181, JapanThe 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 havehttps://doi.org/10.7151/dmgt.1870triangulationsclosed surfacesloosenessk-loosely tightindependence number |
| collection |
DOAJ |
| language |
English |
| format |
Article |
| sources |
DOAJ |
| author |
Nakamoto Atsuhiro Negami Seiya Ohba Kyoji Suzuki Yusuke |
| spellingShingle |
Nakamoto Atsuhiro Negami Seiya Ohba Kyoji Suzuki Yusuke Looseness and Independence Number of Triangulations on Closed Surfaces Discussiones Mathematicae Graph Theory triangulations closed surfaces looseness k-loosely tight independence number |
| author_facet |
Nakamoto Atsuhiro Negami Seiya Ohba Kyoji Suzuki Yusuke |
| author_sort |
Nakamoto Atsuhiro |
| title |
Looseness and Independence Number of Triangulations on Closed Surfaces |
| title_short |
Looseness and Independence Number of Triangulations on Closed Surfaces |
| title_full |
Looseness and Independence Number of Triangulations on Closed Surfaces |
| title_fullStr |
Looseness and Independence Number of Triangulations on Closed Surfaces |
| title_full_unstemmed |
Looseness and Independence Number of Triangulations on Closed Surfaces |
| title_sort |
looseness and independence number of triangulations on closed surfaces |
| publisher |
Sciendo |
| series |
Discussiones Mathematicae Graph Theory |
| issn |
2083-5892 |
| publishDate |
2016-08-01 |
| description |
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 |
| topic |
triangulations closed surfaces looseness k-loosely tight independence number |
| url |
https://doi.org/10.7151/dmgt.1870 |
| work_keys_str_mv |
AT nakamotoatsuhiro loosenessandindependencenumberoftriangulationsonclosedsurfaces AT negamiseiya loosenessandindependencenumberoftriangulationsonclosedsurfaces AT ohbakyoji loosenessandindependencenumberoftriangulationsonclosedsurfaces AT suzukiyusuke loosenessandindependencenumberoftriangulationsonclosedsurfaces |
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