In 1990, Erdős, Faudree, Rousseau and Schelp proved that for k > 2 every graph with n > k+ 1 vertices and (k− 1)(n−k+ 2) + ( k−2 2 ) + 1 edges contains a subgraph of minimum degree k on at most n − √ n/6k3 vertices. They conjectured that it is possible to remove at least kn many vertices and remain with a subgraph of minimum degree k, for some k > 0. We make progress towards their conjecture by...

The width ∆T of the deconfinement transition region is shown to influence strongly the flow structure in the (Landau–) hydrodynamical expansion of a quark–gluon plasma. For a sharp first order transition (∆T = 0) the mixed phase is rather longlived, with a lifetime that has a maximum when the initial energy density is at the phase boundary between mixed and pure quark–gluon matter. For increasi...

The simplest way to overcome the problem is to change formulation. Recall that in [1] we extended the given directed graph G* with one source (s) and two sinks slightly the graph G to a (t and t ). 1 2 Further, our formulation restricted the out degree of the source s to one. Here we modify the directed graph by allowing only one sink et) and restricting the out degree of the source s to at mos...

We propose a new pivot selection technique for symmetric indefinite factorization of sparse matrices. Such factorization should maintain both sparsity and numerical stability of the factors, both of which depend solely on the choices of the pivots. Our method is based on the minimum degree algorithm and also considers the stability of the factors at the same time. Our experiments show that our ...

Let D be a digraph with vertex set V(D) .For vertex v V(D), the degree of v, denoted by d(v), is defined as the minimum value if its out-degree  and its in-degree . Now let D be a digraph with minimum degree  and edge-connectivity If  is real number, then the zeroth-order general Randic index is defined by   .  A digraph is maximally edge-connected if . In this paper we present sufficient condi...

For every $n\in\mathbb{N}$ and $k\geqslant2$, it is known that $k$-edge-colouring of the complete graph on $n$ vertices contains a monochromatic connected component order at least $\frac{n}{k-1}$. $k\geqslant3$, can be replaced by $G$ with $\delta(G)\geqslant(1-\varepsilon_k)n$ for some constant $\varepsilon_k$. In this paper, we show maximum possible value $\varepsilon_3$ $\frac16$. This dispr...