TY - JOUR UR - http://lib.ugent.be/catalog/pug01:6921573 ID - pug01:6921573 LA - eng TI - Alternating plane graphs PY - 2015 JO - (2015) ARS MATHEMATICA CONTEMPORANEA SN - 1855-3966 PB - 2015 AU - Althöfer, Ingo AU - Haugland, Jan Kristian AU - Scherer, Karl AU - Schneider, Frank AU - Van Cleemput, Nicolas WE02 002001123134 802000034893 0000-0001-9689-9302 AB - A plane graph is called alternating if all adjacent vertices have different degrees, and all neighboring faces as well. Alternating plane graphs were introduced in 2008. This paper presents the previous research on alternating plane graphs.There are two smallest alternating plane graphs, having 17 vertices and 17 faces each. There is no alternating plane graph with 18 vertices, but alternating plane graphs exist for all cardinalities from 19 on. From a small set of initial building blocks, alternating plane graphs can be constructed for all large cardinalities. Many of the small alternating plane graphs have been found with extensive computer help.Theoretical results on alternating plane graphs are included where all degrees have to be from the set {3,4,5}. In addition, several classes of “weak alternating plane graphs” (with vertices of degree 2) are presented. ER -Download RIS file
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001 | 6921573 | ||
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008 | 150903s2015------------------------eng-- | ||
022 | a 1855-3966 | ||
024 | a 000364936900001 2 wos | ||
024 | a 1854/LU-6921573 2 handle | ||
040 | a UGent | ||
245 | a Alternating plane graphs | ||
260 | c 2015 | ||
520 | a A plane graph is called alternating if all adjacent vertices have different degrees, and all neighboring faces as well. Alternating plane graphs were introduced in 2008. This paper presents the previous research on alternating plane graphs.There are two smallest alternating plane graphs, having 17 vertices and 17 faces each. There is no alternating plane graph with 18 vertices, but alternating plane graphs exist for all cardinalities from 19 on. From a small set of initial building blocks, alternating plane graphs can be constructed for all large cardinalities. Many of the small alternating plane graphs have been found with extensive computer help.Theoretical results on alternating plane graphs are included where all degrees have to be from the set {3,4,5}. In addition, several classes of “weak alternating plane graphs” (with vertices of degree 2) are presented. | ||
598 | a A1 | ||
100 | a Althöfer, Ingo | ||
700 | a Haugland, Jan Kristian | ||
700 | a Scherer, Karl | ||
700 | a Schneider, Frank | ||
700 | a Van Cleemput, Nicolas u WE02 0 002001123134 0 802000034893 0 0000-0001-9689-9302 | ||
650 | a Mathematics and Statistics | ||
653 | a alternating degrees | ||
653 | a Plane graph | ||
653 | a exhaustive search | ||
653 | a heuristic search | ||
773 | t ARS MATHEMATICA CONTEMPORANEA g Ars Math. Contemp. 2015. 8 (2) p.337-363 q 8:2<337 | ||
856 | 3 Full Text u https://biblio.ugent.be/publication/6921573/file/6921591 z [open] y 584-3877-1-PB.pdf | ||
920 | a article | ||
852 | x WE b WE02 | ||
922 | a UGENT-WE |
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