42441601
Hamiltonian uniform subset graphs
The uniform subset graph G(n, k, t) is defined to have all k-subsets of an n-set as vertices and edges joining k-subsets intersecting at t elements. We conjecture that G(n, k, t) is hamiltonian when it is different from the Petersen graph and does possess cycles. We verify this conjecture for k − t = 1, 2, 3 and for suitably large n when t = 0, 1.
12831347
Equitable Coloring and the Maximum Degree
Abstract Let Δ(G) denote the maximum degree of a graph G . The equitable Δ-coloring conjecture asserts that a connected graph G is equitably Δ( G )-colorable if it is different from K m , C 2 m + 1 and K 2 m + 1,2 m + 1 for all m ⩾ 1. This conjecture is established for graphs G satisfying Δ( G ) ⩾ | G |/2 or Δ( G ) ⩽ 3.
42366271
A Note on the m-Bounded Chromatic Number of a Tree
Abstract The m-bounded chromatic number of a graph G is the smallest number of colors required for a proper coloring of G in which each color is used at most m times. We will establish an exact formula for the m -bounded chromatic number of a tree.
16166391
Linear k-arboricities on trees
Abstract For a fixed positive integer k, the linear k-arboricity lak(G) of a graph G is the minimum number l such that the edge set E(G) can be partitioned into l disjoint sets and that each induces a subgraph whose components are paths of lengths at most k. This paper studies linear k-arboricity from an algorithmic point of view. In particular, we present a linear-time algorithm to determine whether a tree T has lak(T)⩽m.
14354011
A study of the total chromatic number of equibipartite graphs
Abstract The total chromatic number χ t ( G ) of a graph G is the least number of colors needed to color the vertices and edges of G so that no adjacent vertices or edges receive the same color, no incident edges receive the same color as either of the vertices it is incident with. In this paper, we obtain some results of the total chromatic number of the equibipartite graphs of order 2 n with maximum degree n − 1. As a part of our results, we disprove the biconformability conjecture.
16547141
Edge domination in complete partite graphs
Abstract An edge dominating set in a graph G is a set of edges D such that every edge not in D is adjacent to an edge of D . An edge domatic partition of a graph G =( V , E ) is a collection of pairwise-disjoint edge dominating sets of G whose union is E . The maximum size of an edge domatic partition of G is called the edge domatic number . In this paper, we study the edge domatic number of the complete partite graphs and give the answers for balanced complete partite graphs and complete split graphs .
2315502
SMARTPAPER: An Interactive and User Friendly Sketching System
This paper describes an interactive sketching system for 3D design/modeling that diverts from the conventional menu-and-button interfaces of CAD tools. The system, dubbed SMARTPAPER, offers a unified sketching environment that supports direct sketching as well as gestured sketching with more emphasis on the former to encourage natural sketching styles. SMARTPAPER also provides a unified 2D and 3D drawing domain by allowing the user to sketch directly on a 3D model in addition to the usual 2D sketching from scratch. A natural sketching experience is offered by supporting casual sketching consisting of wiggly, discontinuous, overlapping strokes. The system is empowered by an array of seamlessly integrated 2D and 3D features such as 2D sketch cleaning, 3D reconstruction from 2D sketch, 3D transformations, sketching on 3D, and conventional 3D CSG operations like cutting and joining. The key to the success of SMARTPAPER is efficient and robust 3D reconstruction from a single freehand 2D sketch with minimal hints. We have employed and improved Lipson’s optimization method, originally designed for offline reconstruction of engineering drawings, in our interactive system by leveraging additional clues obtained by interaction during sketching.
1980658
Geometric Sieving: Automated Distributed Optimization of 3D Motifs for Protein Function Prediction
Determining the function of all proteins is a recurring theme in modern biology and medicine, but the sheer number of proteins makes experimental approaches impractical. For this reason, current efforts have considered in silico function prediction in order to guide and accelerate the function determination process. One approach to predicting protein function is to search functionally uncharacterized protein structures (targets), for substructures with geometric and chemical similarity (matches), to known active sites (motifs). Finding a match can imply that the target has an active site similar to the motif, suggesting functional homology. 
 
An effective function predictor requires effective motifs – motifs whose geometric and chemical characteristics are detected by comparison algorithms within functionally homologous targets (sensitive motifs), which also are not detected within functionally unrelated targets (specific motifs). Designing effective motifs is a difficult open problem. Current approaches select and combine structural, physical, and evolutionary properties to design motifs that mirror functional characteristics of active sites. 
 
We present a new approach, Geometric Sieving (GS), which refines candidate motifs into optimized motifs with maximal geometric and chemical dissimilarity from all known protein structures. The paper discusses both the usefulness and the efficiency of GS. We show that candidate motifs from six well-studied proteins, including α-Chymotrypsin, Dihydrofolate Reductase, and Lysozyme, can be optimized with GS to motifs that are among the most sensitive and specific motifs possible for the candidate motifs. For the same proteins, we also report results that relate evolutionarily important motifs with motifs that exhibit maximal geometric and chemical dissimilarity from all known protein structures. Our current observations show that GS is a powerful tool that can complement existing work on motif design and protein function prediction.
38323853
Content-based Language Models for Spoken Document Retrieval
Spoken document retrieval (SDR) has been extensively studied in recent years because of its potential use in navigating large multimedia collections in the near future. This paper presents a novel concept of applying content-based language models to spoken document retrieval. In an example task for retrieval of Mandarin Chinese broadcast news data, the content-based language models, either trained on automatic transcriptions of spoken documents or adapted from baseline language models using automatic transcriptions of spoken documents, were used to create more accurate recognition results and indexing terms from both spoken documents and speech queries. We report on some interesting findings obtained in this research.
11015337
Composite subset measures
Measures are numeric summaries of a collection of data records produced by applying aggregation functions. Summarizing a collection of subsets of a large dataset, by computing a measure for each subset in the (typically, user-specified) collection is a fundamental problem. The multidimensional data model, which treats records as points in a space defined by dimension attributes, offers a natural space of data subsets to be considered as summarization candidates, and traditional SQL and OLAP constructs, such as GROUP BY and CUBE, allow us to compute measures for subsets drawn from this space. However, GROUP BY only allows us to summarize a limited collection of subsets, and CUBE summarizes all subsets in this space. Further, they restrict the measure used to summarize a data subset to be a one-step aggregation, using functions such as SUM, of field-values in the data records.In this paper, we introduce composite subset measures, computed by aggregating not only data records but also the measures of other related subsets. We allow summarization of naturally related regions in the multidimensional space, offering more flexibility than either GROUP BY or CUBE in the choice of what data subsets to summarize. Thus, our framework allows more meaningful summaries to be computed for a targeted collection of data subsets.We propose an algebra called AW-RA and an equivalent pictorial language called aggregation workflows. Aggregation workflows allow for intuitive expression of composite measure queries, and the underlying algebra is designed to facilitate efficient multiscan execution. We describe an evaluation framework based on multiple passes of sorting and scanning over the original dataset. In each pass, several measures are evaluated simultaneously, and dependencies between these measures and containment relationships between the underlying subsets of data are orchestrated to reduce the memory footprint of the computation. We present a performance evaluation that demonstrates the benefits of our approach.
13073706
Graph homotopy and Graham homotopy
Abstract Simple-homotopy for cell complexes is a special type of topological homotopy constructed by elementary collapses and elementary expansions. In this paper, we introduce graph homotopy for graphs and Graham homotopy for hypergraphs and study the relation between the two homotopies and the simple-homotopy for cell complexes. The graph homotopy is useful to describe topological properties of discretized geometric figures, while the Graham homotopy is essential to characterize acyclic hypergraphs and acyclic relational database schemes.