scholarly journals On Edge Colorings with at Least q Colors in Every Subset of p Vertices

10.37236/1553 ◽  
2000 ◽  
Vol 8 (1) ◽  
Author(s):  
Gábor N. Sárközy ◽  
Stanley Selkow
Keyword(s):  
Edge Coloring ◽  
Log P ◽  
Q Value ◽  
P Values ◽  
Edge Colorings

For fixed integers $p$ and $q$, an edge coloring of $K_n$ is called a $(p, q)$-coloring if the edges of $K_n$ in every subset of $p$ vertices are colored with at least $q$ distinct colors. Let $f(n, p, q)$ be the smallest number of colors needed for a $(p, q)$-coloring of $K_n$. In [3] Erdős and Gyárfás studied this function if $p$ and $q$ are fixed and $n$ tends to infinity. They determined for every $p$ the smallest $q$ ($= {p \choose 2} - p + 3$) for which $f(n,p,q)$ is linear in $n$ and the smallest $q$ for which $f(n,p,q)$ is quadratic in $n$. They raised the question whether perhaps this is the only $q$ value which results in a linear $f(n,p,q)$. In this paper we study the behavior of $f(n,p,q)$ between the linear and quadratic orders of magnitude. In particular we show that that we can have at most $\log p$ values of $q$ which give a linear $f(n,p,q)$.

scholarly journals A note on compact and compact circular edge-colorings of graphs

2008 ◽  
Vol Vol. 10 no. 3 (Graph and Algorithms) ◽  
Author(s):  
Dariusz Dereniowski ◽  
Adam Nadolski
Keyword(s):  
Approximation Algorithm ◽  
Decision Problem ◽  
Edge Coloring ◽  
Exact Algorithm ◽  
Weighted Graphs ◽  
Edge Colorings ◽  
Odd Cycle ◽  
International Audience ◽  
Np Complete ◽  
Odd Cycles

Graphs and Algorithms International audience We study two variants of edge-coloring of edge-weighted graphs, namely compact edge-coloring and circular compact edge-coloring. First, we discuss relations between these two coloring models. We prove that every outerplanar bipartite graph admits a compact edge-coloring and that the decision problem of the existence of compact circular edge-coloring is NP-complete in general. Then we provide a polynomial time 1:5-approximation algorithm and pseudo-polynomial exact algorithm for compact circular coloring of odd cycles and prove that it is NP-hard to optimally color these graphs. Finally, we prove that if a path P2 is joined by an edge to an odd cycle then the problem of the existence of a compact circular coloring becomes NP-complete.

Rm values of phenols. Their relation with log P values and activity

1975 ◽  
Vol 18 (9) ◽  
pp. 868-873 ◽  
Author(s):  
G. L. Biagi ◽  
O. Gandolfi ◽  
M. C. Guerra ◽  
A. M. Barbaro ◽  
G. Cantelli-Forti
Keyword(s):  
Log P ◽  
P Values

scholarly journals Preparation and Hydro-Lipophilic Properties of Selected Novel Chlorinated and Brominated N-Arylcinnamamides

Proceedings ◽  
2019 ◽  
Vol 41 (1) ◽  
pp. 11
Author(s):  
Tomas Strharsky ◽  
Timotej Jankech ◽  
Jiri Kos ◽  
Kristina Maricakova ◽  
Andrea Pramukova ◽  
...  
Keyword(s):  
High Performance ◽  
Chemical Structure ◽  
Antimicrobial Agents ◽  
Reversed Phase ◽  
Log P ◽  
Organic Modifier ◽  
Chromatography Method ◽  
P Values ◽  
Liquid Chromatography Method ◽  
Derivatives Of

A series of six di- and tri-halogenated N-arylcinnamanilides designed as anti-inflammatory and antimicrobial agents was prepared and characterized. Since it is known that lipophilicity significantly influences the biological activity of compounds, the hydro-lipophilic properties of these di- and tri-substituted N-arylcinnamanilides were investigated in the study. All the discussed derivatives of cinnamic acid were analyzed using the reversed-phase high performance liquid chromatography method to measure lipophilicity. The procedure was performed under isocratic conditions with methanol as an organic modifier in the mobile phase using an end-capped non-polar C18 stationary reversed-phase column. In the present study, the correlations between the logarithm of the capacity factor k and log P/Clog P values calculated in various ways as well as the relationships between the lipophilicity and the chemical structure of the studied compounds are discussed.

scholarly journals The distance to the Large Magellanic Cloud from first overtone RR Lyrae variables

2004 ◽  
Vol 193 ◽  
pp. 180-183
Author(s):  
A.V. Muzzin ◽  
C.M. Clement ◽  
D.R. Alves ◽  
Keyword(s):  
Fourier Coefficients ◽  
Large Magellanic Cloud ◽  
Light Curves ◽  
Log P ◽  
Distance Modulus ◽  
P Values ◽  
Rr Lyrae ◽  
Visual Distance ◽  
Bona Fide ◽  
Absolute Magnitudes

AbstractFourier coefficients have been derived for the V and R light curves of 330 bona fide RR Lyrae first-overtone (RR1) pulsators in 16 MACHO fields near the bar of the LMC. We use the Fourier phase parameter ɸ31 and log P values to select a subsample of these stars which are similar to the RR1s in the Galactic globular cluster M5. Assuming that the M5-like stars in the LMC have absolute magnitudes comparable to the HB stars in M5, we use independent studies to derive their mean absolute V magnitude and compute a visual distance modulus of μLMC = 18.43 ± 0.06 (statistical) ±0.16 (systematic). By selecting stars on the basis of their light curve parameters, we are able to derive a distance modulus that does not depend on the somewhat poorly determined Mv – [Fe/H] relation for RR Lyr stars.

scholarly journals Preparation and Hydro-Lipophilic Properties of Methoxylated and Methylated 1-Hydroxynaphthalene-2-Carboxanilides

Proceedings ◽  
2018 ◽  
Vol 9 (1) ◽  
pp. 43 ◽  
Author(s):  
Iva Kapustikova ◽  
Tomas Gonec ◽  
Jiri Kos ◽  
Ewelina Spaczynska ◽  
Michal Oravec ◽  
...  
Keyword(s):  
Mobile Phase ◽  
High Performance ◽  
Chemical Structure ◽  
Reversed Phase ◽  
Log P ◽  
Organic Modifier ◽  
Chromatography Method ◽  
P Values ◽  
Liquid Chromatography Method ◽  
Substituted 1

A series of variously methoxylated and methylated N-aryl-1-hydroxynaphthalene-2-carboxanilides was prepared and characterized as potential anti-invasive agents. As it is known that lipophilicity significantly influences the biological activity of compounds, the hydro-lipophilic properties of these mono-, di- and tri-substituted 1-hydroxynaphthalene-2-carboxanilides are investigated in the study. All the discussed hydroxynaphthalene derivatives were analyzed using the reversed-phase, high-performance liquid chromatography method, to measure lipophilicity. The procedure was performed under isocratic conditions with methanol as an organic modifier in the mobile phase, using an end-capped, non-polar C18 stationary reversed-phase column. The present study discusses the correlations between the logarithm of the capacity factor k and log P/Clog P values, calculated in various ways, as well as the relationships between the lipophilicity and the chemical structure of the studied compounds.

scholarly journals A comparative study concerning chromatographic retention and computed partition coefficients of some precursors of peraza crown ethers

2010 ◽  
Vol 8 (6) ◽  
pp. 1203-1209 ◽  
Author(s):  
Cristina Onişor ◽  
Gabriela Blăniţă ◽  
Maria Coroş ◽  
Monica Bucşa ◽  
Mircea Vlassa ◽  
...  
Keyword(s):  
Comparative Study ◽  
Crown Ethers ◽  
Partition Coefficients ◽  
High Performance ◽  
Correlation Coefficients ◽  
Reversed Phase ◽  
Neural Network Modeling ◽  
Log P ◽  
Chromatographic Retention ◽  
P Values

AbstractRetention indices for some precursors of peraza crown ethers were determined by reversed phase high-performance thin layer chromatography on RP-18 plates with methanol-water in different volume proportions as mobile phase. The Log P values for the same compounds were calculated using different computer programs: SciQSAR, SciLogP, Chem3D Ultra 8.0, XLOGP (based on atom contributions), Chemaxon and KOWWIN (based on atom/fragment contributions), cLogP (based on fragmental contributions), ALOGPS and IAlogP (based on atom-type electrotopological-state indices and neural network modeling). A comparative study concerning lipophilic parameters (RM0, b and ϕ0) and computed partition coefficients has been developed. Taking into account the correlation coefficients between determined and calculated Log P values, it seems that RM0 and b are less suitable than ϕ0 for estimating lipophilicity of the compounds investigated, and cLogP and ALOGPS provide the best correlations with experimental values.

On the Adjacent Vertex Distinguishing Proper Edge Colorings of Several Classes of Complete 5-Partite Graphs

2013 ◽  
Vol 333-335 ◽  
pp. 1452-1455
Author(s):  
Chun Yan Ma ◽  
Xiang En Chen ◽  
Fang Yang ◽  
Bing Yao
Keyword(s):  
Chromatic Number ◽  
Edge Coloring ◽  
Adjacent Vertex ◽  
Chromatic Numbers ◽  
Edge Colorings ◽  
Proper Edge Coloring ◽  
Minimum Number

A proper $k$-edge coloring of a graph $G$ is an assignment of $k$ colors, $1,2,\cdots,k$, to edges of $G$. For a proper edge coloring $f$ of $G$ and any vertex $x$ of $G$, we use $S(x)$ denote the set of thecolors assigned to the edges incident to $x$. If for any two adjacent vertices $u$ and $v$ of $G$, we have $S(u)\neq S(v)$,then $f$ is called the adjacent vertex distinguishing proper edge coloring of $G$ (or AVDPEC of $G$ in brief). The minimum number of colors required in an AVDPEC of $G$ is called the adjacent vertex distinguishing proper edge chromatic number of $G$, denoted by $\chi^{'}_{\mathrm{a}}(G)$. In this paper, adjacent vertex distinguishing proper edge chromatic numbers of several classes of complete 5-partite graphs are obtained.

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