Dirac's conjecture on K5-subdivisions
โ Scribed by Carsten Thomassen
- Publisher
- Elsevier Science
- Year
- 1997
- Tongue
- English
- Weight
- 145 KB
- Volume
- 165-166
- Category
- Article
- ISSN
- 0012-365X
No coin nor oath required. For personal study only.
๐ SIMILAR VOLUMES
## Abstract A Short proof is given of the theorem that every grph that does not have __K__~4~ as a subcontraction is properly vertex 3โcolorable.
A necessary and sufficient condition for a function to be a generator of dynamical symmetry transformations in hamiltonian formalism is derived and presented in two forms, one of which involves an evolution operator connecting hamiltonian and lagrangian formalisms. As a particular case gauge transfo
## Abstract A conjecture of Dirac states that every simple graph with __n__ vertices and 3__n__ โ 5 edges must contain a subdivision of __K__~5~. We prove that a topologically minimal counterexample is 5โconnected, and that no minorโminimal counterexample contains __K__~4~ โ __e__. Consequently, Di
## Abstract Rao posed the following conjecture, โLet G be a selfโcomplementary graph of order __p__, ฯ = (d~1~ โฆ dp) be its degree sequence. Then G has a kโfactor if and only if ฯ โ k, = (d1 โ k, โฆ dP โ k) is graphical.โ We construct a family of counterexamples for this conjecture for every k โฉพ 3.