We determine the maximum number of edges that a claw-free graph can have, when its maximum degree and matching number are bounded. This is a famous problem that has been studied on general graphs, and for which there is a tight bound. The graphs achieving this bound contain in most cases an induced copy of K1,3, the claw, which motivates studying the question on claw-free graphs. Note that on g...

here a posteriori error estimate for the numerical solution of nonlinear voltena- hammerstein equations is given. we present an error upper bound for nonlinear voltena-hammastein integral equations, in which the form of nonlinearity is algebraic and develop a posteriori error estimate for the recently proposed method of brunner for these problems (the implicitly linear collocation method).we al...

We introduce the Linear Resource Temporal Network (LRTN), which consists of activities that consume or produce a resource, subject to absolute and relative metric temporal constraints; production and consumption is restricted to linear functions of activity duration. We show how to construct tight bounds for resource availability as a function of time in LRTNs; for a broad class of problems, th...

The enumeration of normal surfaces is a key bottleneck in computational three-dimensional topology. The underlying procedure is the enumeration of admissible vertices of a high-dimensional polytope, where admissibility is a powerful but non-linear and non-convex constraint. The main results of this paper are significant improvements upon the best known asymptotic bounds on the number of admissi...

The engineering profession agrees that present design and quality assurance rules lead to sufficiently safe and economic structures although these rules have been developed widely by trial and error. If safety is quantified in probabilistic terms admissible risks are calibrated against present rules of practice. Unfortunately, large variations in admissible, calibrated risks are found and it is...

A project scheduling problem consists of a finite set of jobs, each with fixed integer duration, requiring one or more resources such as personnel or equipment, and each subject to a set of precedence relations, which specify allowable job orderings, and a set of mutual exclusion relations, which specify jobs that cannot overlap. No job can be interrupted once started. The objective is to minim...

We give an upper bound for the number of different basic feasible solutions generated by Dantzig’s simplex method (the simplex method with the most negative pivoting rule) for LP with bounded variables by extending the result of Kitahara and Mizuno (2010). We refine the analysis by them and improve an upper bound for a standard form of LP. Then we utilize the improved bound for an LP with bound...

We study the behavior of the A∗ search algorithm when coupled with a heuristic h satisfying (1 − 1)h ≤ h ≤ (1 + 2)h, where 1, 2 ∈ [0, 1) are small constants and h∗ denotes the optimal cost to a solution. We prove a rigorous, general upper bound on the time complexity of A∗ search on trees that depends on both the accuracy of the heuristic and the distribution of solutions. Our upper bound is es...

Let ( ) denote the maximum possible number of codewords in a binary code of length and minimum Hamming distance . For large values of , the best known upper bound, for fixed , is the Johnson bound. We give a new upper bound which is at least as good as the Johnson bound for all values of and , and for each there are infinitely many values of for which the new bound is better than the Johnson bo...

A graph G is (m,k)-colourable if its vertices can be coloured with m colours such that the maximum degree of the subgraph induced on vertices receiving the same colour is at most k. The k-defective chromatic number χk(G) is the least positive integer m for which G is (m,k)colourable. Maddox proved that χk(G)+χk(Ḡ) ≤ 5 p 3k+4 whenever G is a triangle-free of order p and k ≥ 0 is an integer. Sima...