32538712
On the sizes of graphs embeddable in surfaces of nonnegative Euler characteristic and their applications to edge choosability
There are two main theorems stated in the introduction section. Theorem A gives upper bounds on the sizes of graphs that are 2-cell embedded in a surface of nonnegative Euler characteristic and contain no cycles of specified lengths. Some of these bounds are used in Theorem B to confirm the List Edge Coloring Conjecture for such graphs with maximum degree exceeding prescribed thresholds.
26709203
The Linear 2-Arboricity of Outerplanar Graphs
9810371
The edge-face choosability of plane graphs
A plane graph G is said to be k-edge-face choosable if, for every list L of colors satisfying |L(x)|=k for every edge and face x, there exists a coloring which assigns to each edge and each face a color from its list so that any adjacent or incident elements receive different colors. We prove that every plane graph G with maximum degree Δ(G) is (Δ(G)+3)-edge-face choosable.
1003852
Upper Bounds of Entire Chromatic Number of Plane Graphs
The entire chromatic number χvef (G) of a plane graph G is the least number of colors assigned to the vertices, edges and faces so that every two adjacent or incident pair of them receive different colors. Kronk and Mitchem (1973) conjectured that χvef (G) ≤ 1 + 4 for every plane graph G. In this paper we prove the conjecture for a plane graph G having χ ′(G) = 1 and give a upper bound χvef (G) ≤ 1+ 5 for all plane graphs, where χ ′(G) and 1 are the chromatic index and the maximum degree of G, respectively.
11186519
Edge-partitions of graphs of nonnegative characteristic and their game coloring numbers
Let G be a graph of nonnegative characteristic and let g(G) and @D(G) be its girth and maximum degree, respectively. We show that G has an edge-partition into a forest and a subgraph H so that (1) @D(H)= =11; (2) @D(H)= =7; (3) @D(H)= =5 or G does not contain 4-cycles and 5-cycles; (4) @D(H)= =11; (2) col"g(G)= =7; (3) col"g(G)= =5 or G contains no 4-cycles and 5-cycles; (4) col"g(G)=<10 if G does not contain 4-cycles.
6853966
Total chromatic number of planar graphs with maximum degree ten
9657581
k-anycast game in selfish networks
Conventionally, the majority of network routing protocols assume that every network terminal or link forwards data for others without any deviation. However, this may not be true when the terminals or links are owned by individual selfish users, who always tries to maximize their own benefits instead of faithfully following a prescribed protocol. In this paper, we propose a new routing protocol, called k-anycast routing, that works well even if network links (or terminals or both) are selfish. In our protocol, the source node first finds a tree that spans k receivers out of a set of possible receivers and pay the relay links to compensate their costs. We prove that every relay link follows the routing protocol: it maximizes its profit when it declares its actual cost
5616933
Techniques for effective vocabulary selection
The vocabulary of a continuous speech recognition (CSR) system is a significant factor in determining its performance. In this paper, we present three principled approaches to select the target vocabulary for a particular domain by trading off between the target out-of-vocabulary (OOV) rate and vocabulary size. We evaluate these approaches against an ad-hoc baseline strategy. Results are presented in the form of OOV rate graphs plotted against increasing vocabulary size for each technique.
10774024
Accurate Classification of Protein Structural Families Using Coherent Subgraph Analysis
Protein structural annotation and classification is an important problem in bioinformatics. We report on the development of an efficient subgraph mining technique and its application to finding characteristic substructural patterns within protein structural families. In our method, protein structures are represented by graphs where the nodes are residues and the edges connect residues found within certain distance from each other. Application of subgraph mining to proteins is challenging for a number reasons: (1) protein graphs are large and complex, (2) current protein databases are large and continue to grow rapidly, and (3) only a small fraction of the frequent subgraphs among the huge pool of all possible subgraphs could be significant in the context of protein classification. To address these challenges, we have developed an information theoretic model called coherent subgraph mining. From information theory, the entropy of a random variable X measures the information content carried by X and the Mutual Information (MI) between two random variables X and Y measures the correlation between X and Y. We define a subgraph X as coherent if it is strongly correlated with every sufficiently large sub-subgraph Y embedded in it. Based on the MI metric, we have designed a search scheme that only reports coherent subgraphs. To determine the significance of coherent protein subgraphs, we have conducted an experimental study in which all coherent subgraphs were identified in several protein structural families annotated in the SCOP database (Murzin et al, 1995). The Support Vector Machine algorithm was used to classify proteins from different families under the binary classification scheme. We find that this approach identifies spatial motifs unique to individual SCOP families and affords excellent discrimination between families.
1884379
Penalty Function Approach for Constrained Convolutive Blind Source Separation
A new approach for convolutive blind source separation(BSS) using penalty functions is proposed in this paper. Motivated by nonlinear programming techniques for the constrained optimization problem, it converts the convolutive BSS into a joint diagonalization problem with unconstrained optimization. Theoretical analyses together with numerical evaluations reveal that the proposed method not only improves the separation performance by significantly reducing the effect of large errors within the elements of covariance matrices at low frequency bins and removes the degenerate solution induced by a null unmixing matrix, but also provides an unified framework to constrained BSS.
1166455
Comparing Graph Representations of Protein Structure for Mining Family-Specific Residue-Based Packing Motifs
We find recurring amino-acid residue packing patterns, or spatial motifs, that are characteristic of protein structural families, by applying a novel frequent subgraph mining algorithm to graph representations of protein three-dimensional structure. Graph nodes represent amino acids, and edges are chosen in one of three ways: first, using a threshold for contact distance between residues; second, using Delaunay tessellation; and third, using the recently developed almost-Delaunay edges. For a set of graphs representing a protein family from the Structural Classification of Proteins (SCOP) database, subgraph mining typically identifies several hundred common subgraphs corresponding to spatial motifs that are frequently found in proteins in the family but rarely found outside of it. We find that some of the large motifs map onto known functional regions in two protein families explored in this study, i.e., serine proteases and kinases. We find that graphs based on almost-Delaunay edges significantly reduce the number of edges in the graph representation and hence present computational advantage, yet the patterns extracted from such graphs have a biological interpretation approximately equivalent to that of those extracted from distance based graphs.