Zobrazeno 1 - 10
of 25
pro vyhledávání: '"R. B. Richter"'
Publikováno v:
Journal of Graph Theory. 79:159-165
We show that a graph-like continuum embeds in some surface if and only if it does not contain one of: a generalized thumbtack; or infinitely many K3, 3s or K5s that are either pairwise disjoint or all have just a single point in common.
Externí odkaz:
https://explore.openaire.eu/search/publication?articleId=doi_________::5b33cb103879af9a24677449dc78df30
https://doi.org/10.1002/jgt.21823
https://doi.org/10.1002/jgt.21823
Publikováno v:
European Journal of Combinatorics. 25(6):785-792
We show that if a very large grid is embedded in a surface, then a large subgrid is embedded in a disc in the surface. This readily implies that: (a) a minor-minimal graph that does not embed in a given surface has no very large grid; and (b) a minor
Externí odkaz:
https://explore.openaire.eu/search/publication?articleId=doi_dedup___::491d765f2ef9b26bab08773bcd7d148a
Publikováno v:
Journal of Graph Theory. 43:79-92
Externí odkaz:
https://explore.openaire.eu/search/publication?articleId=doi_________::9e239349631f916cc74a775a691ca7a3
https://doi.org/10.1002/jgt.10070
https://doi.org/10.1002/jgt.10070
It is very well-known that there are precisely two minimal non-planar graphs: $K_5$ and $K_{3,3}$ (degree 2 vertices being irrelevant in this context). In the language of crossing numbers, these are the only 1-crossing-critical graphs: they each have
Externí odkaz:
https://explore.openaire.eu/search/publication?articleId=doi_dedup___::4433414c0f5e6dedf57d8c966c00e655
Publikováno v:
Journal of Graph Theory. 20:297-308
The orientable genus is determined for any graph that embeds into the projective plane, Σ, to be essentially half of the representativity of any embedding into Σ. In addition, a structure is given for any 3-connected projective planar graph as the
Externí odkaz:
https://explore.openaire.eu/search/publication?articleId=doi_________::f47104d6619b1efc168d6dbebef65377
https://doi.org/10.1002/jgt.3190200305
https://doi.org/10.1002/jgt.3190200305
Autor:
R. B. Richter, C. Thomassen
Publikováno v:
Discrete & Computational Geometry. 13:149-159
It[Figure not available: see fulltext.] and[Figure not available: see fulltext.] are two families of pairwise disjoint simple closed curves in the plane such that each curve in[Figure not available: see fulltext.] intersects each curve in[Figure not
Externí odkaz:
https://explore.openaire.eu/search/publication?articleId=doi_________::eda24e0cf7d3f69bf2bc22f298be9ea4
https://doi.org/10.1007/bf02574034
https://doi.org/10.1007/bf02574034
Publikováno v:
Discrete Mathematics. 126:273-280
We show that every 3-connected planar graph has a circular embedding in some nonspherical surface. More generally, we characterize those planar graphs that have a 2-representative embedding in some nonspherical surface.
Externí odkaz:
https://explore.openaire.eu/search/publication?articleId=doi_dedup___::11b6dd4d8cb07fc64cfef091e7c6f925
https://doi.org/10.1016/0012-365x(94)90271-2
https://doi.org/10.1016/0012-365x(94)90271-2
Autor:
Dan Archdeacon, R. B. Richter
Publikováno v:
Journal of Graph Theory. 14:199-204
A covering is a graph map φ: G→H that is an isomorphism when restricted to the star of any vertex of G. If H is connected then |φ −1 (v)| is constant. This constant is called the fold number. In this paper we prove that if G is a planar graph t
Externí odkaz:
https://explore.openaire.eu/search/publication?articleId=doi_________::5077f1b91ff714b33a68077bec5c996c
https://doi.org/10.1002/jgt.3190140208
https://doi.org/10.1002/jgt.3190140208
Publikováno v:
SIAM Journal on Discrete Mathematics, 20(1), 189-202. Society for Industrial and Applied Mathematics Publications
Tilburg University-PURE
Tilburg University-PURE
It has been long--conjectured that the crossing number cr(K_m,n) of the complete bipartite graph K_m,n equals the Zarankiewicz Number Z(m,n):= floor((m-1)/2) floor(m/2) floor((n-1)/2) floor(n/2). Another long--standing conjecture states that the cros
Externí odkaz:
https://explore.openaire.eu/search/publication?articleId=doi_dedup___::97391086ae3e773bdaefeb71207e6d75
http://arxiv.org/abs/math/0404142
http://arxiv.org/abs/math/0404142
Publikováno v:
Annals of the New York Academy of Sciences. 576:118-124
Externí odkaz:
https://explore.openaire.eu/search/publication?articleId=doi_________::16404bf21afd0c1133bf6903d469c0b0
https://doi.org/10.1111/j.1749-6632.1989.tb16389.x
https://doi.org/10.1111/j.1749-6632.1989.tb16389.x