Color the cycles

The cycles of length k in a complete graph on n vertices are colored in such a way that edge-disjoint cycles get distinct colors. The minimum number of colors is asymptotically determined. © 2013

Media, Aggregators, and the Link Economy: Strategic Hyperlink Formation in Content Networks

A defining property of the World Wide Web is a content site's ability to place virtually costless hyperlinks to third-party content as a substitute or complement to its own content. Costless hyperlinking has enabled new types of players, usually referred to as content aggregators, to successfully enter content ecosystems, attracting traffic and revenue by hosting links to the content of others. This, in turn, has sparked a heated controversy between content creators and aggregators regarding the legitimacy and costs/benefits of uninhibited free linking. To our knowledge, this work is the first to model the complex interplay between content and links in settings where a set of sites compete for traffic. We develop a series of analytical models that distill how hyperlinking affects the (a) incentives of content nodes to produce quality content versus link to third-party content, (b) profits of the various stakeholders, (c) average quality of content that becomes available to consumers, and (d) impact of content aggregators. Our results provide a nuanced view of the so-called link economy, highlighting both the beneficial consequences and the drawbacks of free hyperlinks for content creators and consumers.This paper was accepted by Lorin Hitt, information systems

Multiply intersecting families of sets

AbstractLet [n] denote the set {1,2,…,n}, 2[n] the collection of all subsets of [n] and F⊂2[n] be a family. The maximum of |F| is studied if any r subsets have an at least s-element intersection and there are no ℓ subsets containing t+1 common elements. We show that |F|⩽∑i=0t−sn−si+t+ℓ−st+2−sn−st+1−s+ℓ−2 and this bound is asymptotically the best possible as n→∞ and t⩾2s⩾2, r,ℓ⩾2 are fixed

Butterfly and skipper records from Lebanon (Lepidoptera: Papilionoidea)

Eighty-five specimens of 30 papilionoid species have been collected in Lebanon during entomological expeditions launched in 2015 and 2016 by the joint project of the Hungarian Natural History Museum and the Holy Spirit University of Kaslik. Th e collecting sites and events are listed, and the species annotated. With 23 figures