geoscience.net logo
+ Resolve Article
+ Follow Us
Follow on FacebookFollow on Facebook
Follow on TwitterFollow on Twitter

+ Translate
+ Subscribe to Site Feed
GeoScience Most Shared ContentMost Shared Content

A Combined Logarithmic Bound on the Chromatic Index of Multigraphs


, : A Combined Logarithmic Bound on the Chromatic Index of Multigraphs. Journal of Graph Theory aop(aop)

For a multigraph G, the integer round?up ?(G) of the fractional chromatic index ?f?(G) provides a good general lower bound for the chromatic index ??(G). For an upper bound, Kahn 1996 showed that for any real c> there exists a positive integer N so that ??(G)<f?(G)+c?f?(G) whenever ?f?(G)>N. We show that for any multigraph G with order n and at least one edge, ??(G)??(G)+ log 3/2( min {(n+1)/3,?(G)}). This gives the following natural generalization of Kahn's result: for any positive reals c,e, there exists a positive integer N so that ??(G)<f?(G) + c (?f?(G))e whenever ?f?(G)>N. We also compare the upper bound found here to other leading upper bounds.

US$19.90

DOI: 10.1002/jgt.21670


Other references

Senthil Kumar, P.; Saravanan, A.; Anish Kumar, K.; Yashwanth, R.; Visvesh, S., 2016: Removal of toxic zinc from water/wastewater using eucalyptus seeds activated carbon: non-linear regression analysis. In the present study, a novel activated carbon was prepared from low-cost eucalyptus seeds, which was utilised for the effectively removal of toxic zinc from the water/wastewater. The prepared adsorbent was studied by Fourier transform infrared sp...

Kryukov V.Yu; Pichushkov A.V., 1985: Current aspects of the epidemiology of diphtheria. Sovetskaya Meditsina (7): 57-59

Schairer, E., 1956: Soil facts from forestry fertilizing experiments in the Black Forest and in Oberschwaben.. Leaf analyses at periods of up to 50 years after. mammal applications to larch and spruce on sandy humous soils indicated that Ca, P and K losses from the soils had been small. Growth was most favourable when CaCOg + basic slag were applied. Where...

Ebert, R.V.; Borden, C.W.; Hall, W.H.; Gold, D., 1955: A study of hypotension produced by meningococcus toxin. Meningococcus toxin was given to unanesthetized dogs. Hypotension and a decrease in cardiac output were pro-duced. Blood volume did not decrease significantly. Right and left atrial pressures and pulmonary arterial pressure decreased. A small hemo...

He, D.; Chung, M.; Chan, E.; Alleyne, T.; Ha, K.C.H.; Miao, M.; Stahl, R.J.; Keeley, F.W.; Parkinson, J., 2007: Comparative genomics of elastin: Sequence analysis of a highly repetitive protein. Due to the low complexity associated with their sequences, uncovering the evolutionary and functional relationships in highly repetitive proteins such as elastin, spider silks, resilin and abductin represents a significant challenge. Using the pol...

D.M.mbro, A.; Ferlin, A.; D.T.ni, L.; Selice, R.; Caretta, N.; Foresta, C., 2010: Endothelial progenitor cells as a new cardiovascular risk factor in Klinefelter's syndrome. Klinefelter syndrome (KS) is associated with a significant reduced life expectancy (2.1 years) including greater mortality from cardiovascular diseases. Underlying causes that may involve low levels of testosterone as well as the extra X chromosom...

Sushko B.S., 1988: Automated method for the intravital polarographic determination of the tissue oxygen diffusion coefficient. An automatic system for estimating O2 diffusion coefficients (DO2) and oxygen tension (pO2) for 5-6 s is developed to characterize the diffusion component of the oxygen transport in animal tissues on the basis of the theory on O2 diffusion to the...

D'alterio, Joseph C., 2000: Method and apparatus for molding and baking food. An apparatus for compressing and baking fluid food under pressure to form unified shaped products has a heated metal mold bottom with a cavity and a heated metal mold top connected to the piston rod of a pneumatic or hydraulic cylinder positioned...

Ishii, H.; Kimura, K.; Harada, O., 1964: Stress And Auditory Characteristics Of The Rat. Sound stimulation of 300 cps to 100,000 cps was applied to rats, and the cochlear microphonics were recorded from the round window. Thus, the characteristics of the auditory sensation of the rat were investigated. It was found that the greatest au...

Møller, H.U.; Ridgway, A.E., 1990: Granular corneal dystrophy Groenouw type I. A report of a probable homozygous patient. A case of severe granular corneal dystrophy is described. The patient, who is most probably homozygous for the dominantly inherited dystrophy gene, is the product of a first cousin marriage with both parents mildly affected by the same dystrophy....