No abstract

We prove that every triangle-free planar graph on n vertices with maximum degree three has an independent set with size at least 3 8 n. This was suggested and later conjectured by Albertson, Bollobás, and Tucker.

In 1995, Paul Erdös and András Gyárfás conjectured that for every graph of minimum degree at least 3, there exists a non-negative integer $m$ such that $G$ contains a simple cycle of length $2^m$. In this paper, we prove that the conjecture holds for 3-connected cubic planar graphs. The proof is long, computer-based in parts, and employs the Discharging Method in a novel way.

Purpose This paper aims to present recently published resources on information literacy and library instruction through an extensive annotated bibliography of publications covering all library types. Design/methodology/approach This paper annotates English-language periodical articles, monographs, dissertations and other materials on library instruction and information literacy published in 2017 in over 200 journals, magazines, books and other sources. Findings The paper provides a brief description for all 590 sources. Originality/value The information may be used by librarians and interested parties as a quick reference to literature on library instruction and information literacy.

No abstract