Contractions of 6-connected toroidal graphs
نویسندگان
چکیده
منابع مشابه
5-Connected Toroidal Graphs are Hamiltonian-Connected
The problem on the Hamiltonicity of graphs is well studied in discrete algorithm and graph theory, because of its relation to traveling salesman problem (TSP). Starting with Tutte’s result, stating that every 4-connected planar graph is Hamiltonian, several researchers have studied the Hamiltonicity of graphs on surfaces. Extending Tutte’s technique, Thomassen proved that every 4-connected plan...
متن کاملFive-Connected Toroidal Graphs Are Hamiltonian
It is well known that not all 3-connected planar graphs are hamiltonian. Whitney [10] proved that every triangulation of the sphere with no separating triangles is hamiltonian. Tutte [9] proved that every 4-connected planar graph has a Hamilton cycle. Extending Tutte's technique, Thomassen [8] proved that every 4-connected planar graph is in fact Hamilton connected. (A small omission in [8] was...
متن کاملMinimum Tenacity of Toroidal graphs
The tenacity of a graph G, T(G), is dened by T(G) = min{[|S|+τ(G-S)]/[ω(G-S)]}, where the minimum is taken over all vertex cutsets S of G. We dene τ(G - S) to be the number of the vertices in the largest component of the graph G - S, and ω(G - S) be the number of components of G - S.In this paper a lower bound for the tenacity T(G) of a graph with genus γ(G) is obtained using the graph's connec...
متن کاملminimum tenacity of toroidal graphs
the tenacity of a graph g, t(g), is dened by t(g) = min{[|s|+τ(g-s)]/[ω(g-s)]}, where the minimum is taken over all vertex cutsets s of g. we dene τ(g - s) to be the number of the vertices in the largest component of the graph g - s, and ω(g - s) be the number of components of g - s.in this paper a lower bound for the tenacity t(g) of a graph with genus γ(g) is obtained using the graph's...
متن کاملK6 minors in large 6-connected graphs
Jørgensen conjectured that every 6-connected graph G with no K6 minor has a vertex whose deletion makes the graph planar. We prove the conjecture for all sufficiently large graphs. 8 April 2005, revised 22 May 2009. Partially supported by NSF under Grant No. DMS-0200595. Partially supported by NSF under Grants No. DMS-0200595 and. DMS-0354742.
متن کاملذخیره در منابع من
با ذخیره ی این منبع در منابع من، دسترسی به آن را برای استفاده های بعدی آسان تر کنید
ژورنال
عنوان ژورنال: Journal of Combinatorial Theory, Series B
سال: 2007
ISSN: 0095-8956
DOI: 10.1016/j.jctb.2006.09.003