Existence and embeddings of partial Steiner triple systems of order ten with cubic leaves

Denote the set of 21 non-isomorphic cubic graphs of order 10 by L. We first determine precisely which L is an element of L occur as the leave of a partial Steiner triple system, thus settling the existence problem for partial Steiner triple systems of order 10 with cubic leaves. Then we settle the embedding problem for partial Steiner triple systems with leaves L is an element of L. This second result is obtained as a corollary of a more general result which gives, for each integer v greater than or equal to 10 and each L is an element of L, necessary and sufficient conditions for the existence of a partial Steiner triple system of order v with leave consisting of the complement of L and v - 10 isolated vertices. (C) 2004 Elsevier B.V. All rights reserved.

Physiological evidence for reproductive suppression in the introduced population of brown tree snakes (Boiga irregularis) on Guam

Introduced species are an increasingly pervasive problem. While studies on the ecology and behavior of these pests are numerous, there is relatively little known of their physiology, specifically their reproductive and stress physiology. One of the best documented introduced pest species is the brown tree snake, Boiga irregularis, which was introduced onto the Pacific island of Guam sometime around World War II. The snake is responsible for severely reducing Guam's native vertebrates. We captured free-living individuals throughout the year and measured plasma levels of stress and sex hormones in an effort to determine when they were breeding. These data were compared to reproductive cycles from a captive population originally collected from Guam. Free-living individuals had chronically elevated plasma levels of the stress hormone corticosterone and basal levels of sex steroids and a remarkably low proportion were reproductively active. These data coincide with evidence that the wild population may be in decline. Captive snakes, had low plasma levels of corticosterone with males displaying a peak in plasma testosterone levels during breeding. Furthermore, we compared body condition between the free-living and captive snakes from Guam and free-living individuals captured from their native range in Australia. Male and female free-living snakes from Guam exhibited significantly reduced body condition compared to free-living individuals from Australia. We suggest that during the study period, free-living brown tree snakes on Guam were living under stressful conditions, possibly due to overcrowding and overexploitation. of food resources, resulting in decreased body condition and suppressed reproduction. (C) 2004 Elsevier Ltd. All rights reserved.

Steiner triple systems with two disjoint subsystems

It is shown that there exists a triangle decomposition of the graph obtained from the complete graph of order v by removing the edges of two vertex disjoint complete subgraphs of orders u and w if and only if u, w, and v are odd, ((v)(2)) - ((u)(2)) - ((w)(2)) equivalent to 0 (mod 3), and v >= w + u + max {u, w}. Such decompositions are equivalent to group divisible designs with block size 3, one group of size u, one group of size w, and v - u - w groups of size 1. This result settles the existence problem for Steiner triple systems having two disjoint specified subsystems, thereby generalizing the well-known theorem of Doyen and Wilson on the existence of Steiner triple systems with a single specified subsystem. (c) 2005 Wiley Periodicals, Inc.