We prove that χ(G) ≤ max { ω(G),∆2(G), 5 6 (∆(G) + 1) } for every graph G with ∆(G) ≥ 3. Here ∆2 is the parameter introduced by Stacho that gives the largest degree that a vertex v can have subject to the condition that v is adjacent to a vertex whose degree is at least as large as its own. This upper bound generalizes both Brooks’ Theorem and the Ore-degree version of Brooks’ Theorem.

abstract water retention curve (wrc) is a fundamental property of soil. it is used to evaluate available water, permeability, drainage and movement of solutes. despite numerous studies on wrc of soils abroad, no local study has been carried out on charmahal-va-bakhtiari soils. the objective of this study was to compare the quality of fitting of several wrc models to lordegan soils and to select...

Abstract Brooks and Makover developed a combinatorial model of random hyperbolic surfaces by gluing certain ideal triangles. In this paper, we show that for any $\epsilon>0$, as the number triangles goes to infinity, generic surface in Brooks–Makover’s has Cheeger constant less than $\frac {3}{2\pi }+\epsilon $.

Let G be a connected graph with maximum degree k (other than a complete graph or odd cycle), let W be a precolored set of vertices in G inducing a subgraph F , and let D be the minimum distance in G between components of F . If the components of F are complete graphs and D ≥ 8 (for k ≥ 4) or D ≥ 10 (for k = 3), then every proper k-coloring of F extends to a proper k-coloring of G. If the compon...

STUDY DESIGN Biomechanical comparison of 5 atlantoaxial posterior arthrodesis techniques. OBJECTIVE To assess the relative value of different posterior wire constructs when one or two transarticular screws are used. SUMMARY OF BACKGROUND DATA A combination of Gallie or Brooks techniques and 2 posterior transarticular screws has been shown to be effective for atlantoaxial arthrodesis. Anatom...

PURPOSE To assess the effectiveness of Brooks' posterior stabilisation and fusion for the unstable atlantoaxial joint due to congenital dysplastic dens and trauma. METHODS We retrospectively studied records of 54 patients (36 males and 18 females; age range, 3-58 years) who underwent Brooks' posterior stabilisation procedure between March 1975 and December 1999, at the Catholic University of ...

29. Brooks, G., Evans, A. T., Aitken, A. & Evans, F. J. (1987) Cancer Lett. 38,165-170 Evans, A. T., Brooks, G. & Evans, F. J. (1990) Cancer Lett. 49,2529 Evans, F. J., Kinghorn, A. D. & Schmidt, R. J. (1975) Acta Pharmacol. Toxicol. 37,250-256 Tapley, P. M. & Murray, A. W. (1985) Eur. J. Biochem. 151,419-423 Edwards, M. C., Williamson, E. M., Formakong, E., Brooks, G. & Evans, F. J. (1987) Bio...