For a graph $G$, let $f(G)$ denote the size of maximum cut in $G$. The problem estimating as function number vertices and edges $G$ has long history was extensively studied last fifty years. In this paper we propose an approach, based on semidefinite programming, to prove lower bounds $f(G)$. We use approach find large cuts graphs with few triangles $K_r$-free graphs.

Hajnal, A. and N. Sauer, Cut-sets in infinite graphs and partial orders. Discrete Mathematics 117 (1993) 113-125. The set S c V(U) is a cut-set of the vertex v of a graph 9 if v is not adjacent to any vertex in S and, for every maximal clique C of Q, ({v} u S) n C # 0. S is a cut-set of the element v of a partial order 9 if S is a cut-set of v in the comparability graph of 8. Given upper bounds...

statement of problem: biomechanics of the human dentition is inherently complex. purpose: the aim of this study is to investigate, in vitro, the creep and the recovery of dentin under static uniaxial compressive stress conditions. materials and methods: specimens of cylindrical morphology were prepared from recently extracted non-carious lower molar teeth, such that the average tubule orientati...

The recently introduced graph parameter tree-cut width plays a similar role with respect to immersions as the treewidth minors. In this paper, we provide first algorithmic applications of hard combinatorial problems. Tree-cut is known be lower-bounded by function treewidth, but it can much larger and hence has potential facilitate efficient solution problems that are not fixed-parameter tractab...

Given an undirected, edge-weighted connected graph, the k-cut problem is to partition the vertex set into k non-empty connected components so as to minimize the total weight of edges whose end points are in different components. We present a combinatorial polynomial-time 2-approximation algorithm for the k-cut problem. We use a La-grangean relaxation (also suggested by Barahona [2]) to reduce t...

An indirect-ELISA for the diagnosis of mixed gastrointestinal (GI) nematode infection comprising Oesophagostomum, Haemonchus and Trichuris species was standardized using crude somatic antigen of Oesophagostomum columbianum (CSAg-Oc) and sera of slaughtered goats with known parasitological status including Oesophagostomum, Haemonchus, and <em...

The supermodular covering knapsack set is the discrete upper level set of a non-decreasing supermodular function. Submodular and supermodular knapsack sets arise naturally when modeling utilities, risk and probabilistic constraints on discrete variables. In a recent paper Atamtürk and Narayanan [6] study the lower level set of a non-decreasing submodular function. In this complementary paper we...

In this paper we introduce the concept of strong total domination in fuzzy graphs. We determine the strong total domination number for several classes of fuzzy graphs. A lower bound and an upper bound for the strong total domination number in terms of strong domination number is obtained. Strong total domination in fuzzy trees is studied. A necessary and sufficient condition for the set of fuzz...

The supermodular covering knapsack set is the discrete upper level set of a non-decreasing supermodular function. Submodular and supermodular knapsack sets arise naturally when modeling utilities, risk and probabilistic constraints on discrete variables. In a recent paper Atamtürk and Narayanan [6] study the lower level set of a non-decreasing submodular function. In this complementary paper we...

The minimum cut problem for an undirected edge-weighted graph asks us to divide its set of nodes into two blocks while minimizing the weight sum of the cut edges. Here, we introduce a linear-time algorithm to compute near-minimum cuts. Our algorithm is based on cluster contraction using label propagation and Padberg and Rinaldi’s contraction heuristics [SIAM Review, 1991]. We give both sequenti...