We prove the analogue of Turán’s Theorem in random graphs with edge probability p(n) À n−1/(k−1.5). With probability 1 − o(1), one needs to delete approximately 1 k−1–fraction of the edges in a random graph in order to destroy all cliques of size k.

We show that for every probability p with 0 < p < 1, computation of all-terminal graph reliability with edge failure probability p requires time exponential in Ω(m/ log m) for simple graphs of m edges under the Exponential Time Hypothesis.

Select n points uniformly at random from a unit square, and then form a random graph on these points by adding an edge joining each pair independently with probability p. We show that for every fixed > 0, if p < 1 − , then with probability approaching 1 as n becomes large, the resulting embedded graph has unbounded stretch factor.

Simple Stochastic Game nondeterminism nondeterminism probability probability nondeterminism nondeterminism probability 1 Definitions Markov Chain (MC) Definition 1. A Markov Chain ((S, E), δ) is a graph (S, E) with a function δ : S → D(S) that maps every state to a probability distribution of successor states. There is an edge between two states s, t in S iff the probability of going from s to ...

We analyze a model of fault-tolerant systems in a probabilistic setting, exemplified by a simple routing problem in networks. We introduce a randomized variant of a model called the “sabotage game”, where an agent, called “Runner”, and a probabilistic adversary, “Nature”, act in alternation. Runner generates a path from a given start vertex of the network, traversing one edge in each move, whil...

In the classical Erdős–Rényi model of random graphs, when the number of edges is proportional to the number of vertices, the degree distribution is approximately Poisson with a tail decreasing even faster than exponentially. However, in many real life networks power law degree distributions were observed with different exponents. To introduce a more realistic model for the evolution of random n...

In this research paper, we present a novel frame work for handling $m$-polar information by combining the theory of $m-$polar fuzzy  sets with graphs. We introduce certain types of edge regular $m-$polar fuzzy graphs and edge irregular $m-$polar fuzzy graphs. We describe some useful properties of edge regular, strongly edge irregular and strongly edge totally irregular $m-$polar fuzzy graphs. W...

l’tlt: probIc:rn of dztc~ctin~ iri:,c:il::ity c!~arlges in images is canonical in \ isIon. lXi;e del,ectlou opc.1 :ltc,rs arc typ]Lally designed to optimally estimate first or second derival.ivr over some (usually small) support. Other criteria such as output signal to noise ratio or bandwidth have also been argued for. This paper describes an attempt to formulate a set of edge detection criter...

‎Suppose $n$ is a fixed positive integer‎. ‎We introduce the relative n-th non-commuting graph $Gamma^{n} _{H,G}$‎, ‎associated to the non-abelian subgroup $H$ of group $G$‎. ‎The vertex set is $Gsetminus C^n_{H,G}$ in which $C^n_{H,G} = {xin G‎ : ‎[x,y^{n}]=1 mbox{~and~} [x^{n},y]=1mbox{~for~all~} yin H}$‎. ‎Moreover‎, ‎${x,y}$ is an edge if $x$ or $y$ belong to $H$ and $xy^{n}eq y^{n}x$ or $x...