876 research outputs found
On Hamilton decompositions of infinite circulant graphs
No full textThe natural infinite analogue of a (finite) Hamilton cycle is a two-way-infinite Hamilton path (connected spanning 2-valent subgraph).
Although it is known that every connected 2k-valent infinite circulant graph has a two-way-infinite Hamilton path, there exist many such graphs that do not have a decomposition into k edge-disjoint two-way-infinite Hamilton paths. This contrasts with the finite case where it is conjectured that every 2k-valent connected circulant graph has a decomposition into k edge-disjoint Hamilton cycles. We settle the problem of decomposing 2k-valent infinite circulant graphs into k edge-disjoint two-way-infinite Hamilton paths for k=2, in many cases when k=3, and in many other cases including where the connection set is ±{1,2,...,k} or ±{1,2,...,k - 1, 1,2,...,k + 1}
Living Books
No full textOne of the most delightful experiences I have had in a long time. There are two modes for experiencing this program. One runs through the twelve pages one by one, with plenty of animation and music for each event in the story. The other is especially entertaining. The viewer can play with each page, clicking on various objects in the individual picture. Rows of carrots turn into dancers, and tomatoes on the vine turn into a vocal group. Other carrots take off like space missiles. Click on the water and you are liable to see a fish jump up and fly around a bit before bringing the program and picture back to the starting point. Gives new meaning for me to the word interactive. I love it! The boxed CD-ROM comes with a booklet by the same title.This is a hardbound book (hard cover)Language note: English and SpanishProduct Managers: Todd Power and Liza Weiman. English and Spanish. Product Design: Mark Schlichting. Art Direction: Bridget Erdman
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