The Nash-Williams Conjecture and the Dominating Cycle Conjecture
نویسندگان
چکیده
منابع مشابه
Graph minors XXIII. Nash-Williams' immersion conjecture
We define a quasi-order of the class of all finite hypergraphs, and prove it is a well-quasi-order. This has two corollaries of interest: • Wagner’s conjecture, proved in a previous paper, states that for every infinite set of finite graphs, one of its members is a minor of another. The present result implies the same conclusion even if the vertices or edges of the graphs are labelled from a we...
متن کاملContractible subgraphs, Thomassen's conjecture and the dominating cycle conjecture for snarks
We show that the conjectures by Matthews and Sumner (every 4-connected claw-free graph is hamiltonian), by Thomassen (every 4-connected line graph is hamiltonian) and by Fleischner (every cyclically 4-edge-connected cubic graph has either a 3-edgecoloring or a dominating cycle), which are known to be equivalent, are equivalent with the statement that every snark (i.e. a cyclically 4-edge-connec...
متن کاملThe Nash Conjecture for Threefolds
Nash conjectured in 1952 that every compact differentiable manifold can be realized as the set of real points of a real algebraic variety which is birational to projective space. This paper announces the negative solution of this conjecture in dimension 3. The proof shows that in fact very few 3manifolds can be realized this way.
متن کاملApproximation theorems and Nash conjecture
© Mémoires de la S. M. F., 1974, tous droits réservés. L’accès aux archives de la revue « Mémoires de la S. M. F. » (http:// smf.emath.fr/Publications/Memoires/Presentation.html) implique l’accord avec les conditions générales d’utilisation (http://www.numdam.org/legal.php). Toute utilisation commerciale ou impression systématique est constitutive d’une infraction pénale. Toute copie ou impress...
متن کاملA counterexample to the dominating set conjecture
The metric polytope metn is the polyhedron associated with all semimetrics on n nodes and defined by the triangle inequalities xij − xik − xjk ≤ 0 and xij + xik + xjk ≤ 2 for all triples i, j, k of {1, . . . , n}. In 1992 Monique Laurent and Svatopluk Poljak conjectured that every fractional vertex of the metric polytope is adjacent to some integral vertex. The conjecture holds for n ≤ 8 and, i...
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: The Electronic Journal of Combinatorics
سال: 2020
ISSN: 1077-8926
DOI: 10.37236/5505