Randomized Communication versus Partition Number

2018 ◽  
Vol 10 (1) ◽  
pp. 1-20 ◽  
Author(s):  
Mika Göös ◽  
T. S. Jayram ◽  
Toniann Pitassi ◽  
Thomas Watson
Keyword(s):  
Partition Number

scholarly journals Clique coverings of graphs V: maximal-clique partitions

1982 ◽  
Vol 25 (3) ◽  
pp. 337-356 ◽  
Author(s):  
N.J. Pullman ◽  
H. Shank ◽  
W.D. Wallis
Keyword(s):  
Maximal Clique ◽  
Maximal Degree ◽  
Open Problems ◽  
Partition Number

A maximal-clique partition of a graph G is a way of covering G with maximal complete subgraphs, such that every edge belongs to exactly one of the subgraphs. If G has a maximal-clique partition, the maximal-clique partition number of G is the smallest cardinality of such partitions. In this paper the existence of maximal-clique partitions is discussed – for example, we explicitly describe all graphs with maximal degree at most four which have maximal-clique partitions - and discuss the maximal-clique partition number and its relationship to other clique covering and partition numbers. The number of different maximal-clique partitions of a given graph is also discussed. Several open problems are presented.

Regiospecific analysis of fractions of bovine milk fat triacylglycerols with the same partition number

Lipids ◽  
1998 ◽  
Vol 33 (12) ◽  
pp. 1195-1201 ◽  
Author(s):  
Paul Angers ◽  
Édith Tousignant ◽  
Armand Boudreau ◽  
Joseph Arul
Keyword(s):  
Milk Fat ◽  
Bovine Milk ◽  
Partition Number ◽  
Regiospecific Analysis

scholarly journals Biclique Covers and Partitions

10.37236/3595 ◽  
2014 ◽  
Vol 21 (1) ◽  
Author(s):  
Trevor Pinto
Keyword(s):  
Analogous Result ◽  
Intersection Graph ◽  
Intersection Graphs ◽  
Partition Number ◽  
Additional Information ◽  
Open Questions ◽  
Dimensional Cube

The biclique cover number (resp. biclique partition number) of a graph $G$, $\mathrm{bc}(G$) (resp. $\mathrm{bp}(G)$), is the least number of bicliques - complete bipartite subgraphs - that are needed to cover (resp. partition) the edges of $G$.The local biclique cover number (resp. local biclique partition number)  of a graph $G$, $\mathrm{lbc}(G$) (resp. $\mathrm{lbp}(G)$), is the least $r$ such that there is a cover (resp. partition) of the edges of $G$ by bicliques with no vertex in more than $r$ of these bicliques.We show that $\mathrm{bp}(G)$ may be bounded in terms of $\mathrm{bc}(G)$, in particular, $\mathrm{bp}(G)\leq \frac{1}{2}(3^\mathrm{bc(G)}-1)$. However, the analogous result does not hold for the local measures. Indeed, in our main result, we show that $\mathrm{lbp}(G)$ can be arbitrarily large, even for graphs with $\mathrm{lbc}(G)=2$. For such graphs, $G$, we try to bound $\mathrm{lbp}(G)$ in terms of additional information about biclique covers of $G$. We both answer and leave open questions related to this.There is a well known link between biclique covers and subcube intersection graphs. We consider the problem of finding the least $r(n)$ for which every graph on $n$ vertices can be represented as a subcube intersection graph in which every subcube has dimension $r$. We reduce this problem to the much studied question of finding the least $d(n)$ such that every graph on $n$ vertices is the intersection graph of subcubes of a $d$-dimensional cube.

The Strong Perfect Graph Conjecture for Planar Graphs

1973 ◽  
Vol 25 (1) ◽  
pp. 103-114 ◽  
Author(s):  
Alan Tucker
Keyword(s):  
Chromatic Number ◽  
Planar Graphs ◽  
Independent Set ◽  
Independent Sets ◽  
Clique Number ◽  
Perfect Graph ◽  
Stability Number ◽  
Partition Number ◽  
Minimum Number ◽  
The Stability

A graph G is called γ-perfect if ƛ (H) = γ(H) for every vertex-generated subgraph H of G. Here, ƛ(H) is the clique number of H (the size of the largest clique of H) and γ(H) is the chromatic number of H (the minimum number of independent sets of vertices that cover all vertices of H). A graph G is called α-perfect if α(H) = θ(H) for every vertex-generated subgraph H of G, where α (H) is the stability number of H (the size of the largest independent set of H) and θ(H) is the partition number of H (the minimum number of cliques that cover all vertices of H).

HPLC and GLC analysis of the triglyceride composition of bovine, ovine and caprine milk fat

1990 ◽  
Vol 57 (4) ◽  
pp. 517-526 ◽  
Author(s):  
Luis J. R. Barron ◽  
M. Teresa G. Hierro ◽  
Guillermo Santa-María
Keyword(s):  
Fatty Acids ◽  
Molecular Species ◽  
Milk Fat ◽  
Triglyceride Composition ◽  
Qualitative Composition ◽  
Triglyceride Fraction ◽  
Partition Number ◽  
Caprine Milk ◽  
Total Triglyceride

SummaryA total of 116 molecular species of triglycerides were identified in milk fat, using a combination of HPLC and GLC. Triglyceride composition was predicted from the random composition, which was calculated on the basis of the mole fractions of the main fatty acids making up the total triglyceride fraction. The qualitative composition of the milk fat was similar in cows', ewes' and goats' milk. In all three milks the partition number of the main triglycerides was 46, but the proportions of the triglycerides with partition numbers of 34, 38, 42, and 48 exhibited substantial differences among the milks of the three species.

scholarly journals ON THE FACTORIAL MOMENT ANALYSIS OF HIGH ENERGY EXPERIMENTAL DATA WITH NONINTEGER PARTITION NUMBER

1999 ◽  
Vol 14 (23) ◽  
pp. 3687-3697 ◽  
Author(s):  
GANG CHEN ◽  
LIANSHOU LIU ◽  
YANMIN GAO
Keyword(s):  
Experimental Data ◽  
Phase Space ◽  
Factorial Moment ◽  
High Energy ◽  
Moment Analysis ◽  
Systematic Method ◽  
Particle Correlations ◽  
Partition Number ◽  
Self Consistency

It is pointed out that in doing the factorial moment analysis with noninteger partition M of phase–space, the influence of the phase–space variation of two (or more) particle correlations has to be considered carefully. In this paper this problem is studied and a systematic method is developed to minimize this influence. The efficiency and self-consistency of this method are shown using the data of 250 GeV /c π+p and K+p collisions from the NA22 experiment as example.

scholarly journals On Extremal Set Partitions in Cartesian Product Spaces

1993 ◽  
Vol 2 (3) ◽  
pp. 211-220 ◽  
Author(s):  
Rudolf Ahlswede ◽  
Ning Cai
Keyword(s):  
Cartesian Product ◽  
Product Spaces ◽  
Minimal Size ◽  
Set Partitions ◽  
Partition Number ◽  
Vertex Set ◽  
Extremal Set

The partition number of a product hypergraph is introduced as the minimal size of a partition of its vertex set into sets that are edges. This number is shown to be multiplicative if all factors are graphs with all loops included.

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