Beyond Ohba's Conjecture: A bound on the choice number of kk-chromatic graphs with nn vertices

Let $\text{ch}(G)$ denote the choice number of a graph $G$ (also called "list chromatic number" or "choosability" of $G$). Noel, Reed, and Wu proved the conjecture of Ohba that $\text{ch}(G)=\chi(G)$ when $|V(G)|\le 2\chi(G)+1$. We extend this to a general upper bound: $\text{ch}(G)\le \max\{\chi(G),\lceil({|V(G)|+\chi(G)-1})/{3}\rceil\}$. Our result is sharp for $|V(G)|\le 3\chi(G)$ using Ohba's examples, and it improves the best-known upper bound for $\text{ch}(K_{4,\dots,4})$.Comment: 14 page

Give Her A Game Of Jolly

https://digitalcommons.library.umaine.edu/mmb-vp/5587/thumbnail.jp

Ev\u27rything\u27s Funny To Me : Laughing Song

https://digitalcommons.library.umaine.edu/mmb-vp/3094/thumbnail.jp

My Cosey Corner Girl

https://digitalcommons.library.umaine.edu/mmb-vp/3301/thumbnail.jp

Vegetation Patterns in and among Pannes (Calcareous Intradunal Ponds) at the Indiana Dunes National Lakeshore, Indiana

The relationships between plant species composition and dispersion, water chemistry and water depth/depth to water table were studied in five calcareous intradunal ponds (pannes) bordering the southern tip of Lake Michigan. The panne systems contained eight plant species threatened and endangered in Indiana. The aquatic zone was dominated by Chara, the pond edge by Rhynchospora capillacea, Juncus balticus and Utricularia cornuta, and the area surrounding the pond by Hypericum kalmianum. The water chemistry was typical of hardwater ponds in the area, probably affecting species composition but not species dispersion within the pannes. A significant correlation between the first axis scores from a reciprocal-averaging ordination and water depth/depth to water was demonstrated. Panne species are fitted to a model based on hydrology proposed by van der Laan for dune-slack vegetation in the Netherlands

Valuation of Tree Aesthetics on Small Urban-Interface Properties

A model was developed to predict the value contribution of forest condition on small urban-wildland interface properties. Sample data were collected on property transactions in the Lake Tahoe Basin of California between 1990 and 1994. A variant of the stand density index (SDI) and a tree health measure were added to a list of traditional property characteristics (i.e., location, house size, lot size) to express the influence of tree care on property value. These aesthetic characteristics were statistically significant despite the expected dominant influence of the traditional characteristics. Values for the forest density and health characteristics were estimated and reveal a contribution to property value between 5% and 20%