We prove that there exists a function f ðcÞ such that the vertex set of every f ðcÞ-connected graph G can be partitioned into sets S and T such that each vertex in S has at least c neighbours in T and both G1⁄2S and G1⁄2T are c-connected. This implies that there exists a function gðc;HÞ such that every gðc;HÞ-connected graph contains a subdivision TH of H so that G VðTHÞ is c-connected. We also...

Introduction: Mental arithmetic analysis based on Electroencephalogram (EEG) signal for monitoring the state of the user’s brain functioning can be helpful for understanding some psychological disorders such as attention deficit hyperactivity disorder, autism spectrum disorder, or dyscalculia where the difficulty in learning or understanding the arithmetic exists. Most mental arithmetic recogni...

In the parameterized problem MAXLIN2-AA[k], we are given a system with variables x1, . . . , xn consisting of equations of the form ∏ i∈I xi = b, where xi, b ∈ {−1, 1} and I ⊆ [n], each equation has a positive integral weight, and we are to decide whether it is possible to simultaneously satisfy equations of total weight at leastW/2+ k, whereW is the total weight of all equations and k is the p...

This is best possible in the sense that we cannot additionally require the entire bipartite subgraph of G between S and T to have large minimum degree. Applying the result of Mader that every graph of sufficiently large average degree contains a subdivision of a given graph H to the graph G[S] obtained by the above theorem, it immediately follows that every highly connected graph G contains a “...

We study Abelian sandpiles on graphs of the form G×I, where G is an arbitrary finite connected graph, and I ⊂ Z is a finite interval. We show that for any fixed G with at least two vertices, the stationary measures μI = μG×I have two extremal weak limit points as I ↑ Z. The extremal limits are the only ergodic measures of maximum entropy on the set of infinite recurrent configurations. We show ...

Conjecture number 747 of Graffiti (circa 1992) states that the average distance of a simple, connected graph is not more than half the maximum order of an induced bipartite subgraph. Recently, P. Hansen et al. settled this conjecture by showing that the average distance is not more than half the maximum order of an induced forest. Moreover, they conjectured that the average distance is not more...

Mobility Metrics of the connectivity graphs with fixed number of nodes have been presented in several research studies over the last three years. More realistic mobility models that are derived from real user traces challenge the assumption of the connectivity graph with fixed number of nodes, but they rather show that wireless nodes posses dynamic membership (nodes join and leave the simulatio...

The scale-fee networks, having connectivity distribution P (k) ∼ k−α (where k is the site connectivity), is very resilient to random failures but fragile to intentional attack. The purpose of this paper is to find the network design guideline which can make the robustness of the network to both random failures and intentional attack maximum while keeping the average connectivity < k > per node ...

Given a set V of n sensor node distributed on a 2-dimensional plane and a source node s ∈ V, the interference problem deals with assigning transmission range to each v ∈ V such that the members in V maintain connectivity predicate P , and the maximum/total interference is minimum. We propose algorithm for both minimizing maximum interference andminimizing total interference of the networks. For...