Zobrazeno 1 - 10
of 230
pro vyhledávání: '"Carsten Thomassen"'
Publikováno v:
Discrete Mathematics & Theoretical Computer Science, Vol Vol. 17 no. 1, Iss Graph Theory (2015)
Graph Theory
Externí odkaz:
https://doaj.org/article/aff3f38c797c4330b49bc48bf79033d2
Autor:
Carsten Thomassen
Publikováno v:
Journal of Combinatorial Theory, Series B. 161:15-20
Externí odkaz:
https://explore.openaire.eu/search/publication?articleId=doi_________::ff4f8ba65c9482118b1ca971102ab714
https://doi.org/10.1016/j.jctb.2023.01.005
https://doi.org/10.1016/j.jctb.2023.01.005
Autor:
Carsten Thomassen
Publikováno v:
Thomassen, C 2023, ' Exponentially many 3-colorings of planar triangle-free graphs with no short separating cycles ', Journal of Combinatorial Theory. Series B, vol. 158, pp. 301-312 . https://doi.org/10.1016/j.jctb.2021.01.009
The number of proper vertex-3-colorings of every triangle-free planar graph with n vertices and with no separating cycle of length 4 or 5 is at least 2 n / 17700000 . On the other hand, for infinitely many n, there exists a triangle-free planar graph
Externí odkaz:
https://explore.openaire.eu/search/publication?articleId=doi_dedup___::719c7c01b760ed6a642188acba679a77
https://doi.org/10.1016/j.jctb.2021.01.009
https://doi.org/10.1016/j.jctb.2021.01.009
Publikováno v:
Special Matrices, Vol 9, Iss 1, Pp 112-118 (2021)
Guterman, A, Kreines, E & Thomassen, C 2021, ' Linear transformations of tropical matrices preserving the cyclicity index ', Special Matrices, vol. 9, no. 1, pp. 112-118 . https://doi.org/10.1515/spma-2020-0128
Guterman, A, Kreines, E & Thomassen, C 2021, ' Linear transformations of tropical matrices preserving the cyclicity index ', Special Matrices, vol. 9, no. 1, pp. 112-118 . https://doi.org/10.1515/spma-2020-0128
We combine matrix theory and graph theory methods to give a complete characterization of the surjective linear transformations of tropical matrices that preserve the cyclicity index. We show that there are non-surjective linear transformations that p
Externí odkaz:
https://explore.openaire.eu/search/publication?articleId=doi_dedup___::88b71ee7f8e44349c22d46940fc12434
https://doi.org/10.1515/spma-2020-0128
https://doi.org/10.1515/spma-2020-0128
Autor:
Carsten Thomassen, Kathie Cameron
Publikováno v:
Cameron, K & Thomassen, C 2020, ' Cycles containing all the odd-degree vertices ', Journal of Combinatorial Theory. Series B, vol. 143, pp. 219-225 . https://doi.org/10.1016/j.jctb.2019.12.003
The number of cycles in a graph containing any fixed edge and also containing all vertices of odd degree is odd if and only if all vertices have even degree. If all vertices have even degree this is a theorem of Shunichi Toida. If all vertices have o
Externí odkaz:
https://explore.openaire.eu/search/publication?articleId=doi_dedup___::c87efd6c1eddb58a0a83147ca4a6ac96
https://doi.org/10.1016/j.jctb.2019.12.003
https://doi.org/10.1016/j.jctb.2019.12.003
Publikováno v:
Alahmadi, A, Aldred, R E L & Thomassen, C 2020, ' Cycles in 5-connected triangulations ', Journal of Combinatorial Theory. Series B, vol. 140, pp. 27-44 . https://doi.org/10.1016/j.jctb.2019.04.005
We show that in 5-connected planar and projective planar triangulations on n vertices, the number of Hamiltonian cycles grows exponentially with n. The result is best possible in the sense that 4-connected triangulations on n vertices on any fixed su
Externí odkaz:
https://explore.openaire.eu/search/publication?articleId=doi_dedup___::0a5f47334d162101ad30fd14f7557cd0
https://doi.org/10.1016/j.jctb.2019.04.005
https://doi.org/10.1016/j.jctb.2019.04.005
Publikováno v:
van Aardt, S A, Burger, A P, Frick, M, Thomassen, C & de Wet, J P 2019, ' Hamilton cycles in sparse locally connected graphs ', Discrete Applied Mathematics, vol. 257 . https://doi.org/10.1016/j.dam.2018.10.031
A graph G is locally connected if for every υ ε (G) the open neighbourhood N(υ) of υ is nonempty and induces a connected graph in G. We characterize locally connected graphs of order n with less than 2n edges and show that for any natural number
Externí odkaz:
https://explore.openaire.eu/search/publication?articleId=doi_dedup___::88ea99c63ec453612eb94bfebfcc1e05
https://doi.org/10.1016/j.dam.2018.10.031
https://doi.org/10.1016/j.dam.2018.10.031
Autor:
Klas Markström, Carsten Thomassen
Publikováno v:
Markström, K & Thomassen, C 2021, ' Partite Turán-densities for complete r −uniform hypergraphs on r + 1 vertices ', Journal of Combinatorics, vol. 12, no. 2, pp. 235-245 . https://doi.org/10.4310/JOC.2021.v12.n2.a3
In this paper we investigate density conditions for finding a complete r-uniform hypergraph K(r)r+1 on r + 1 vertices in an (r + 1)-partite runiform hypergraph G. First we prove an optimal condition in terms of the densities of the (r + 1) induced r-
Externí odkaz:
https://explore.openaire.eu/search/publication?articleId=doi_dedup___::18c8578c5512f0706b69bb1ba9d8ef39
https://orbit.dtu.dk/en/publications/60488348-4395-4853-ad6a-6daec8acea24
https://orbit.dtu.dk/en/publications/60488348-4395-4853-ad6a-6daec8acea24
Publikováno v:
Thomassen, C & Zamfirescu, C T 2021, ' 4-regular 4-connected Hamiltonian graphs with a bounded number of Hamiltonian cycles ', Australasian Journal of Combinatorics, vol. 81, no. 2, pp. 334–338 .
Technical University of Denmark Orbit
Technical University of Denmark Orbit
We prove that there exists an infinite family of 4-regular 4-connected Hamiltonian graphs with a bounded number of Hamiltonian cycles. We do not know whether there exists such a family of 5-regular 5-connected Hamiltonian graphs.
Externí odkaz:
https://explore.openaire.eu/search/publication?articleId=dedup_wf_001::bc6b4e5de0130bb6c6ef74230279f256
https://orbit.dtu.dk/en/publications/08f93cfe-4f56-4b0b-bcdb-71ce68621c7a
https://orbit.dtu.dk/en/publications/08f93cfe-4f56-4b0b-bcdb-71ce68621c7a
Autor:
James Davies, Carsten Thomassen
Publikováno v:
Davies, J & Thomassen, C 2020, ' Locally hamiltonian graphs and minimal size of maximal graphs on a surface ', Electronic Journal of Combinatorics, vol. 27, no. 2, P2.25, pp. 1-9 . https://doi.org/10.37236/9286
We prove that every locally Hamiltonian graph with $n\ge 3$ vertices and possibly with multiple edges has at least $3n-6$ edges with equality if and only if it triangulates the sphere. As a consequence, every edge-maximal embedding of a graph $G$ gra
Externí odkaz:
https://explore.openaire.eu/search/publication?articleId=doi_dedup___::642e972e94593e52dc1c07e3d0100f60
https://doi.org/10.37236/9286
https://doi.org/10.37236/9286