4-valent plane graphs with 2-, 3- and 4-gonal faces

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dc.creatorDeza, M.
dc.creatorDutour, M.
dc.creatorShtogrin, M.
dc.date2002-12-27
dc.date2003-08-01
dc.date.accessioned2026-07-07T04:54:05Z
dc.date.available2026-07-07T04:54:05Z
dc.descriptionCall {\em i-hedrite} any 4-valent n-vertex plane graph, whose faces are 2-, 3- and 4-gons only and $p_2+p_3=i$. The edges of an i-hedrite, as of any Eulerian plane graph, are partitioned by its {\em central circuits}, i.e. those, which are obtained by starting with an edge and continuing at each vertex by the edge opposite the entering one. So, any i-hedrite is a projection of an alternating link, whose components correspond to its central circuits. Call an i-hedrite {\em irreducible}, if it has no {\em rail-road}, i.e. a circuit of 4-gonal faces, in which every 4-gon is adjacent to two of its neighbors on opposite edges. We present the list of all i-hedrites with at most 15 vertices. Examples of other results: (i) All i-hedrites, which are not 3-connected, are identified. (ii) Any irreducible i-hedrite has at most i-2 central circuits. (iii) All i-hedrites without self-intersecting central circuits are listed. (iv) All symmetry group of i-hedrites are listed.
dc.description27 pages, 16 figures, submitted to satellite conference (of ISM congress, (2002) Beijing) on Algebra and Combinatorics
dc.identifierhttps://arxiv.org/abs/math/0212351
dc.identifierhttp://arxiv.org/abs/math/0212351
dc.identifier.urihttp://salesiana.dossiersoluciones.com/handle/123456789/66104
dc.subjectGeometric Topology
dc.subjectCombinatorics
dc.subjectPrimary 52B05, 52B10; Secondary 05C30, 05C10
dc.title4-valent plane graphs with 2-, 3- and 4-gonal faces
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