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.
8284293
A note on list improper coloring planar graphs
A graph G is called (k, d)*-choosable if, for every list assignment L satisfying |L(v)| = k for all v ϵ V(G), there is an L-coloring of G such that each vertex of G has at most d neighbors colored with the same color as itself. In this note, we prove that every planar graph without 4-cycles and l-cycles for some l ϵ {5, 6, 7} is (3, 1)*-choosable.
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
26709203
The Linear 2-Arboricity of Outerplanar Graphs
13354529
Edge-pancyclicity of coupled graphs
The coupled graph c(G) of a plane graph G is the graph defined on the vertex set V(G)∪F(G) so that two vertices in c(G) are joined by an edge if and only if they are adjacent or incident in G. We prove that the coupled graph of a 2-connected plane graph is edge-pancyclic. However, there exists a 2-edge-connected plane graph G such that c(G) is not Hamiltonian.
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.
14446380
OP-cluster: clustering by tendency in high dimensional space
Clustering is the process of grouping a set of objects into classes of similar objects. Because of unknownness of the hidden patterns in the data sets, the definition of similarity is very subtle. Until recently, similarity measures are typically based on distances, e.g Euclidean distance and cosine distance. We propose a flexible yet powerful clustering model, namely OP-cluster (Order Preserving Cluster). Under this new model, two objects are similar on a subset of dimensions if the values of these two objects induce the same relative order of those dimensions. Such a cluster might arise when the expression levels of (coregulated) genes can rise or fall synchronously in response to a sequence of environment stimuli. Hence, discovery of OP-Cluster is essential in revealing significant gene regulatory networks. A deterministic algorithm is designed and implemented to discover all the significant OP-Clusters. A set of extensive experiments has been done on several real biological data sets to demonstrate its effectiveness and efficiency in detecting coregulated patterns.
33629250
Robust Visual Tracking Via Incremental Maximum Margin Criterion
Robust visual object tracking is one of the key problems in computer vision. Subspace based tracking method is a promising approach in handling appearance variability. Linear Discriminant Analysis(LDA) has been applied to this problem, but LDA is not a stable algorithm especially for visual tracking. Maximum Margin Criterion(MMC) is a recently proposed discriminant criterion. Its promising specialities make it a better choice for the tracking problem. In this paper, we present a novel subspace tracking algorithm based on MMC. We also proposed an incremental version of the corresponding algorithm so that the tracker can update in realtime. Experiments show our tracking algorithm is able to track objects well under large lighting, pose and expression variation.
11138955
Computing an Almost Minimum Set of Spanning Line Segments of a Polyhedron
A set of spanning line segments (SLS) is a subset of the edges of a finite polyhedron in E3 such that an arbitrary plane intersects the polyhedron if and only if the plane intersects at least one of the line segments of the SLS. In this paper an algorithm is presented for computing an almost minimum set of spanning line segments for an arbitrary polyhedron . When the number of extreme vertices of is odd, the computed SLS is minimum; when the number of extreme vertices of is even, the size of the computed SLS is at most the minimum size plus one. The algorithm has linear-time complexity for a convex polyhedron, hence is optimal in this case; its time complexity is Θ(m log m) for an arbitrary polyhedron, where m is the number of vertices of the polyhedron.
8024755
On Demand Phenotype Ranking through Subspace Clustering
High throughput biotechnologies have enabled scientists to collect a large number of genetic and phenotypic attributes for a large collection of samples. Computational methods are in need to analyze these data for discovering genotype-phenotype associations and inferring possible phenotypes from genotypic attributes. In this paper, we study the problem of on demand phenotype ranking. Given a query sample, for which only its genetic information is available, we want to predict the possible phenotypes it may have, ranked in descending order of their likelihood. This problem is challenging since genotype-phenotype databases are updated often and explicitly mine and maintain all patterns is impractical. We propose an on-demand ranking algorithm that uses a modified pattern-based subspace clustering algorithm to effectively identify the subspaces where these relevant clusters may reside. Using this algorithm, we can compute the clusters and their prediction significance for any phenotypes on the fly. Our experiments demonstrate the efficiency and effectiveness of our algorithm.