According to M. Gardner 9], a snark is a non-trivial cubic graph whose edges cannot be properly coloured by three colours. The problem of what`non-trivial' means is implicitly or explicitly present in most papers on snarks, and is the main motivation of the present paper. Our approach to the discussion is based on the following observation. If G is a snark with a k-edge-cut producing components...

Mutations in the unc-82 locus of Caenorhabditis elegans were previously identified by screening for disrupted muscle cytoskeleton in otherwise apparently normal mutagenized animals. Here we demonstrate that the locus encodes a serine/threonine kinase orthologous to human ARK5/SNARK (NUAK1/NUAK2) and related to the PAR-1 and SNF1/AMP-Activated kinase (AMPK) families. The predicted 1600-amino-aci...

Non-interactive zero-knowledge proofs are a powerful cryptographic primitive used in privacypreserving protocols. We design and build C∅C∅, the first system enabling developers to build efficient, composable, non-interactive zero-knowledge proofs for generic, user-defined statements. C∅C∅ extends state-of-the-art SNARK constructions by applying known strengthening transformations to yield UC-co...

In this paper we show that many snarks have shortest cycle covers of length 43m + c for a constant c, where m is the number of edges in the graph, in agreement with the conjecture that all snarks have shortest cycle covers of length 43m+ o(m). In particular we prove that graphs with perfect matching index at most 4 have cycle covers of length 4 3m and satisfy the (1, 2)-covering conjecture of Z...

Data quality is critical to data analysis because bad data can lead to incorrect conclusions. Problems with data are best detected early, before too much time and eeort are spent ingesting and analyzing it. In this paper, we propose the use of data mining techniques for the automatic detection of data problems commonly encountered in large multivariate data sets. Data mining methods are ideal f...

We present a construction which shows that there is an infinite set of cyclically 4-edge connected cubic graphs on n vertices with no cycle longer than c4n for c4 = 12 13 , and at the same time prove that a certain natural family of cubic graphs cannot be used to lower the shortness coefficient c4 to 0. The graphs we construct are snarks so we get the same upper bound for the shortness coeffici...

In this paper, we study the Goldberg Snarks Gk, twist Goldberg Snarks TGk, Flower snarks Fk, and show the exact value of connected and tree domination number of them. Mathematics Subject Classification: 05C35