A relational structure A satisfies the P(n, k) property if whenever the vertex set of A is partitioned into n nonempty parts, the substructure induced by the union of some k of the parts is isomorphic to A. The P(2, 1) property is just the pigeonhole property, (P), introduced by Cameron, and studied by Bonato, Delić and Cameron. We classify the countable graphs, tournaments, and oriented graphs...

Like its author Ashwin Desai, variously an academic, journalist, teacher, radio talk-show host, activist and member of cricket's national Transformation Monitoring Committee, it is difficult to pigeonhole The Poors of Chatsworth. It is a history ofChatsworth, a narrative of the lives of ordinary South Africans in preand post-apartheid South Africa, an examination of the impact of the ANC govern...

occult hepatitis b (ohb), or persistent hepatitis b virus (hbv) viremia in surface-antigen-hbsag-negative patients, has been recognized as a medical concern during the last decade. the exact magnitude, pathogenesis and clinical relevance of ohb are unclear. this review organizes the published data on ohb and presents an overview of the current hypotheses on ohb's pathogenesis and clinical relev...

Let Ωn be the n -element set consisting of functions that have [n] as both domain and codomain. Since Ωn is finite, it is clear by the pigeonhole principle that, for any f ∈ Ωn, the sequence of compositional iterates f, f , f , f (4) . . . must eventually repeat. Let T(f) be the period of this eventually periodic sequence of functions, i.e. the least positive integer T such that, for all m ≥ n,...

Disruption Tolerant Networks (DTNs) utilize the mobility of nodes and the opportunistic contacts among nodes for data communications. Due to the limitation in network resources such as contact opportunity and buffer space, DTNs are vulnerable to flood attacks in which attackers send as many packets or packet replicas as possible to the network, in order to deplete or overuse the limited network...

Conventional algorithms for Boolean satisfiability (SAT) work within the framework of resolution as a proof system. However it has been known since the 1980s that every resolution proof of the pigeonhole principle (PHPm n ), suitably encoded as a CNF instance, includes exponentially many steps[4]. Therefore SAT solvers based upon the DLL procedure [1] or the DP procedure [2] must take exponenti...

A proof of the (propositional) Craig interpolation theorem for cut-free sequent calculus yields that a sequent with a cut-free proof (or with a proof with cut-formulas of restricted form; in particular, with only analytic cuts) with k inferences has an interpolant whose circuit-size is at most k. We give a new proof of the interpolation theorem based on a communication complexity approach which...

During the last decade, an active line of research in proof complexity has been into the space complexity of proofs and how space is related to other measures. By now these aspects of resolution are fairly well understood, but many open problems remain for the related but stronger polynomial calculus (PC/PCR) proof system. For instance, the space complexity of many standard “benchmark formulas”...