45045031
Well-Covered Vector Spaces of Graphs
For any field ${\bf F}$, the set of all functions $f : V(G) \rightarrow {\bf F}$ whose sum on each maximal independent set is constant forms a vector space over ${\bf F}$. In this paper, we show that the dimension can vary depending on the characteristic of the field. We also investigate the dimensions of these vector spaces and show that while some families, such as chordal graphs, have unbounded dimension, other families, such as nonempty circulant graphs of prime order, have bounded dimension.
28649866
A ramsey type problem concerning vertex colourings
Abstract Let H → k v G denote the fact that for every function π: V ( H ) → {1, …, k } there is an induced subgraph G ′ of H with G ′ ≅ G and V ( G ′) ⊆ π −1 ( i ) for some i . Folkman has shown that for all graphs G and for all positive integers k such a graph H exists. We examine here f ( G , k ), the minimum order of a graph H for which H → k v G . We show that for any fixed integer k ≥ 2 there are positive constants C 1 and C 2 such that C 1 n 2 ≤ max{ f ( G , k ): | V ( G )| = n } ≤ C 2 n 2 log 2 n .
18896340
On the Roots of Chromatic Polynomials
It is proved that the chromatic polynomial of a connected graph with n vertices and m edges has a root with modulus at least (m?1)/(n?2); this bound is best possible for trees and 2-trees (only). It is also proved that the chromatic polynomial of a graph with few triangles that is not a forest has a nonreal root and that there is a graph with n vertices whose chromatic polynomial has a root with imaginary part greater thann/4.
44284809
The strongly connected reliability of complete digraphs
Given a digraph D, consider the model where each vertex is always operational, but the edges are independently operational with probability p. The strongly connected reliability of D, scRel(D, p), is the probability that the spanning subgraph of D consisting of the operational edges is strongly connected. One can view strongly connected reliability as the probability that any vertex can send information to any other vertex, given that edges fail independently. ∗Partially supported by a grant from NSERC. Communicating author.
40600226
The Complexity of Generalized Graph Colorings
Given a graph property P and positive integer k, a P k-coloring of a graph G is an assignment of one of k colors to each vertex of the graph so that the subgraphs induced by each color class have property P. This notion generalizes the standard definition of graph coloring, and has been investigated for many properties. We consider here the complexity of the decision problem. In particular, for the property —G, of not containing an induced subgraph isomorphic to G, we conjecture (and provide strong evidence) that —G k-colorability is NP-complete whenever G has order at least 3 and k ⩾ 2. The techniques rely on new NP-completeness results for hypergraph colorings.
19128559
Bounding the Roots of Independence Polynomials
27879633
To dream the invisible dream
often credited as the creator of the computer game industry, explores the “Relationships between Fun and the Computer Business.” In his article he reminisces, assesses, and projects the effects from the game industry to the computer industry as a whole. Bushnell’s article makes tangible some of the incredible distance we’ve come since the 1970s—from a world where manufacturers didn’t take cathode-ray tube use in the computer industry seriously to a time when most two-year-old children know about computers. Bushnell’s way is to mix lessons learned from the game industry with some as-yet unexplored visions of the way we will play. Henry Lieberman’s work has been that of creating programming and idea presentation environments using his favorite tools of creation objects (his work on actors), dynamic languages (his work on garbage collection), and interactive environments (his work on programming by example). Lieberman’s article, “Intelligent Graphics,” focuses on the inventive serendipity that has and can come out of the relationship between AI and graphics—an idea promoted by yet another pioneer, Muriel Cooper. He also briefly discusses programming by example, a style of interaction that he has been working to demonstrate and promote over the last couple of decades. Ken Kahn also cares deeply about programming languages, having devoted his research career to creating Prolog interpreters, parallel logic systems, and logic-oriented systems. In his article, we see him engaged in his first love, that of creating visual approaches for thinking about programs. Watching programs execute, seeing their structure, seeing their function, organizing them—all with the underlying goal of making programming as easy as child’s play. Finally, as you look to my article, you see me not working or talking about any one idea as I could, but giving a review with some context that describes many of the ideas shaping the way people are using computers today. I hope this eclectic collection of articles can serve as a celebration of our temptations to explore and design the ways computers will help us communicate, create, and record our experiences.
7379001
The ribonuclease P database
The Ribonuclease P Sequence database is a compilation of RNase P sequences, sequence alignments, secondary structures, three-dimensional models, and accessory information. In its initial form, the database contains information on RNase P RNA in bacteria and archaea, and RNase P protein in bacteria. The sequences themselves are presented phylogenetically ordered and aligned. The database also contains secondary structures of bacterial and archaeal RNAs, including specially annotated 'reference' secondary structures of Escherichia coli and Bacillus subtilis RNase P RNAs, a minimum phylogenetic consensus structure, and coordinates for models of three-dimensional structure.
5703219
A Macintosh Hypercard compilation of small subunit ribosomal RNA sequences
Molecular biologists, particularly those working with unicellular organisms, are becoming increasingly aware of the importance of understanding the phylogenetic (evolutionary) relationships between their model systems and other organisms. Currently, the best method for determining quantitatively the phylogenetic relationships in a group of organisms is the analysis of small subunit ribosomal RNA (ssu RNA) sequences (Woese, 1984). To assist in this type of analysis, the Ribosomal RNA Database Project (RDP) collects and distributes ssu rRNA sequences and software for phylogenetic analysis (Olsen et al., 1991). The ssu rRNA sequence stack is collection of almost 500 aligned ssu rRNA sequences taken from the first public release of the RDP sequence collection. The ssu rRNA sequence stack consists of a series of 'cards' each containing the ssu rRNA sequence of a single organism (Figure 1), from which the sequence can be copied (either with or without alignment information) or saved as a text file in GenBank format. Navigation in the stack is via a series of linked phylogenetic trees. Starting with a 'universal tree', clicking on the branch of interest takes the user to increasingly more specific and detailed trees. In the most specific trees, clicking on a branch either takes the user directly to the sequence card (if only one sequence is available representing that group) or presents the user with a pop-up menu of available sequences. Alternatively, the user can choose the desired sequence from a list containing the names of all of the available sequences, or choose to search the sequence names for a specific character string. The ssu rRNA sequence stack is written in Hypertalk v. 2.1, and requires v. 2.0 (or greater) of HyperCard, which in turn requires at least a Macintosh Plus, 1 Mbyte of RAM, the Macintosh operating system v 6.0.5 (or greater), and preferably a hard disk drive. The ssu rRNA sequence stack is available by anonymous FTP from ftp.bio.indiana.edu, by E-mail from the author at jwbrown@bio.indiana.edu or brownjw@iubacs.bitnet, or on floppy disk (enclose a single formatted high-density disk) free of charge on written request to the author.
1800673
Why AM and Eurisko Appear to Work
Seven years ago, the AM program was constructed as an experiment in learning by discovery. Its source of power was a large body of heuristics, rules which guided it toward fruitful topics of investigation, toward profitable experiments to perform, toward plausible hypotheses and definitions. "Other heuristics evaluated those discoveries for utility and "interestingness", and they were added to AM's vocabulary of concepts. AM's ultimate limitation apparently was due to its inability to discover new, powerful, domain-specific heuristics for the various new fields it uncovered. At that time, it seemed straight-forward to simply add Heuretics (the study of heuristics) as one more field in which to let AM explore, observe, define, and develop. That task - learning new heuristics by discovery - turned out to be much more difficult than was realized initially, and we have just now achieved some successes at it. Along the way, it became clearer why AM had succeeded in the first place, and why it was so difficult to use the same paradigm to discover new heuristics. This paper discusses those recent insights. They spawn questions about "where the meaning really resides" in the concepts discovered by AM. This leads to an appreciation of the crucial and unique role of representation in theory formation, a role involving the relationship between Form and Content.
45989851
The Social Life of Documents
Documents are evolving as means for structuring and navigating information space, and resources for constructing and negotiating social space