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### Page 1605 of Mathematical Reviews Vol. , Issue 2003C [page]

2003 Mathematical Reviews
-VCTR-MS; Victoria, BC); McCrea, Devon (3-VCTR-MS; Victoria, BC) Total domination in complements of graphs containing no K4 4.  ...  Summary: “We show that the total domination number of a graph G whose complement, G‘, does not contain K33 is at most 7(G°), except for complete graphs, and graphs belonging to a certain family which is  ...

### Page 649 of Mathematical Reviews Vol. , Issue 94b [page]

1994 Mathematical Reviews
The main result is that if G and its complement have no isolated vertices and diameter(G) > 4, then the lower [upper] global total dominating number equals the lower [upper] total dominating number.  ...  A global total dominating set is a total dominat- ing set for both G and its complement.  ...

### Hard Graphs for the Maximum Clique Problem [chapter]

Cornells Hoede
1988 Annals of Discrete Mathematics
Hard graphs are those graphs for which none of the reduction techniques can be applied. A list of properties of hard graphs is determined.  ...  The resulting graphs do not grow exponentially in order and number. Graphs that allow such a reduction technique are called soft.  ...  Graphs that do not contain K4 -x as induced subgraph are soft.  ...

### Hard graphs for the maximum clique problem

Cornelis Hoede
1988 Discrete Mathematics
Hard graphs are those graphs for which none of the reduction techniques can be applied. A list of properties of hard graphs is determined.  ...  The resulting graphs do not grow exponentially in order and number. Graphs that allow such a reduction technique are called soft.  ...  Graphs that do not contain K4 -x as induced subgraph are soft.  ...

### Page 818 of Mathematical Reviews Vol. , Issue 2002B [page]

2002 Mathematical Reviews
If (at least) one /-total k-dominating set exists, then the /-total k-dominating number y;,4(G) is the minimum cardinality of such a set.  ...  For a graphical parameter u(G), a graph G is u(G)-critical if u(G +e) < 4(G) for every e in the ordinary complement G of G, while G is 4(G)-critical relative to K,, if u(G +e) < u(G) for all e € E(H).  ...

### Small order graph-tree Ramsey numbers

R.J. Faudree, C.C. Rousseau, R.H. Schelp
1988 Discrete Mathematics
With but a few exceptions, the Ramsey number r(G, T) is determined for all connected graphs G with at most five vertices and all trees T.  ...  Clearly this graph contains no K5 -P4 and the blue graph t contains no K(l, 12 -1). Two color the edges of a K 2n and suppose this graph contains no red KS -P4 and no blue K(l, n -1).  ...  Clearly this graph contains no K, -2K, and the blue graph L contains no K(l, n -1).  ...

### Generalized domination and efficient domination in graphs

D.W. Bange, A.E. Barkauskas, L.H. Host, P.J. Slater
1996 Discrete Mathematics
This paper generalizes dominating and efficient dominating sets of a graph. Let G be a graph with vertex set V(G).  ...  Related theoretical and computational questions are considered in the special cases where Y = { -1, 1} or Y = { -1, 0, 1}.  ...  { - 1 , 1 1}, 7r([K,]) < 0 for n >~ 4. Consider the graph [K,] x [-K4].  ...

### Page 7629 of Mathematical Reviews Vol. , Issue 2000k [page]

2000 Mathematical Reviews
Hartnell (3-STMR; Halifax, NS) 2000k:05209 05C69 Klobuéar, Antoaneta Domination numbers of cardinal products. (English summary) Math. Slovaca 49 (1999), no. 4, 387-402.  ...  Summary: “The class of trapezoid graphs is a subclass of cocom- parability graphs and contains both the interval graphs and the permutation graphs.  ...

### Page 72 of Mathematical Reviews Vol. , Issue 97A [page]

1997 Mathematical Reviews
in question emerging as totally singular lines.  ...  We also give an algorithm that computes the kth sphere-of-influence graph of a set of n points in R4 in time O(n2-2/(!+\(4+2)/2))+© + kn log? n), for any e > 0.”  ...

### Page 5668 of Mathematical Reviews Vol. , Issue 88k [page]

1988 Mathematical Reviews
The Ramsey number R(3, 5) = 14 implies that an arbitrary graph G on 14 vertices without triangles contains Ks (the complement of Ks). Even more is true: G contains at least six Ks’s.  ...  A realization of M(p,q) is a 2-coloring of K, such that the total number of red K, and blue K, is exactly M(p,q). In the paper under review all the realizations of M(3, 5) are described.  ...

### Articulation sets in linear perfect matrices I: forbidden configurations and star cutsets

Michele Conforti, M.R. Rao
1992 Discrete Mathematics
We then prove that a graph whose clique-node incidence matrix is linear but not totally unimodular contains a node v such that the removal of v and all its neighbors disconnects the graph.  ...  These results yield a proof of the strong perfect graph conjecture for this class of graphs. Conjecture 1.1. A graph is perfect if and only if its complement is perfect. Conjecture 1.2.  ...  In this paper we study the decomposition of graphs not containing the graph K4 -e of Fig. 1 as an induced subgraph.  ...

### Disjoint Sets in Graphs and its Application to Electrical Networks

Gaol
2011 Journal of Mathematics and Statistics
Approach: This problem was modeled as the vertex covering problems in graphs. The graph modeling of this problem as the minimum vertex covering set problem.  ...  The minimu of a graph cardinality of a degree covering set of a graph G is the degree covering number γP(G). Conclusion: We show that Degree Covering Set (DCS) problem is NP-complete.  ...  The set P is a DCS for two reasons: (i) Base on the definition of DCS that v Vertex in each variable cycle K 4 belongs to P are dominated.  ...

### The Requirements for COMPASS and Paf1 in Transcriptional Silencing and Methylation of Histone H3 in Saccharomyces cerevisiae

J. E. Mueller
2006 Genetics
The Set1-containing complex, COMPASS, methylates histone H3 on lysine 4 (K4) in Saccharomyces cerevisiae.  ...  Despite the preferential association of K4-trimethylated H3 with regions of the genome that are transcribed by RNA polymerase II, transcriptional silencing is one of the few cases in S. cerevisiae where  ...  The authors appreciate the input and contributions of Fred Winston, in whose lab this work was initiated.  ...

### On Polynomial Kernels for Structural Parameterizations of Odd Cycle Transversal [article]

Bart M. P. Jansen, Stefan Kratsch
2011 arXiv   pre-print
Complementing this, we exclude polynomial kernels for OCT parameterized by the distance to outerplanar graphs, conditioned on the assumption that NP \not \subseteq coNP/poly.  ...  On the positive side, we show a polynomial kernel for OCT when parameterized by the vertex deletion distance to the class of bipartite graphs of treewidth at most w (for any constant w); this generalizes  ...  in the B K4 graphs were deleted.  ...

### Total Domination Value in Graphs [article]

Cong X. Kang
2012 arXiv   pre-print
This definition gives rise to a local study of total domination in graphs.  ...  A total dominating set of G of minimum cardinality is called a γ_t(G)-set.  ...  The author greatly appreciates Eunjeong Yi for much valuable help in drawing the figures and in deriving the formulas contained in this paper.  ...
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