26709203
The Linear 2-Arboricity of Outerplanar Graphs
41898252
Vertex-pancyclicity of edge-face-total graphs
The edge-face-total graph r(G) of a plane graph G is the graph defined on the vertex set E(G)∪F(G) so that two vertices in r(G) are joined by an edge if and only if they were adjacent or incident in G. In this paper we prove that (1) the edge-face-total graph of a 2-connected plane graph is vertex-pancyclic and there exists a connected plane graph G with cut vertices such that r(G) is non-Hamiltonian; (2) the line graph of a 2-connected plane graph with at most one face of degree ⩾4 is pancyclic.
207859527
L(p, q)-labelling of K4-minor free graphs
15064123
A new proof of Melnikov's conjecture on the edge-face coloring of plane graphs
In 1975, Melnikov conjectured that the edges and faces of each plane graph G may be colored with Δ(G)+3 colors so that any two adjacent or incident elements receive different colors, where Δ(G) is the maximum degree of G. Two similar, yet independent, proofs of this conjecture have been published recently by Waller (J. Combin. Theory Ser. B 69 (1997) 219) and Sanders and Zhao (Combinatorica 17 (1997) 441). Both proofs made use of the Four-Color Theorem. This paper presents a new proof of Melnikov's conjecture independent of the Four-Color Theorem.
18746420
Bordeaux 3-color conjecture and 3-choosability
A graph G=(V,E) is list L-colorable if for a given list assignment L={L(v):v@?V}, there exists a proper coloring c of G such that c(v)@?L(v) for all v@?V. If G is list L-colorable for every list assignment with |L(v)|>=k for all v@?V, then G is said to be k-choosable. In this paper, we prove that (1) every planar graph either without 4- and 5-cycles, and without triangles at distance less than 4, or without 4-, 5- and 6-cycles, and without triangles at distance less than 3 is 3-choosable; (2) there exists a non-3-choosable planar graph without 4-cycles, 5-cycles, and intersecting triangles. These results have some consequences on the Bordeaux 3-color conjecture by Borodin and Raspaud [A sufficient condition for planar graphs to be 3-colorable. J. Combin. Theory Ser. B 88 (2003) 17-27].
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.
377228
SPIN: mining maximal frequent subgraphs from graph databases
One fundamental challenge for mining recurring subgraphs from semi-structured data sets is the overwhelming abundance of such patterns. In large graph databases, the total number of frequent subgraphs can become too large to allow a full enumeration using reasonable computational resources. In this paper, we propose a new algorithm that mines only maximal frequent subgraphs, i.e. subgraphs that are not a part of any other frequent subgraphs. This may exponentially decrease the size of the output set in the best case; in our experiments on practical data sets, mining maximal frequent subgraphs reduces the total number of mined patterns by two to three orders of magnitude.Our method first mines all frequent trees from a general graph database and then reconstructs all maximal subgraphs from the mined trees. Using two chemical structure benchmarks and a set of synthetic graph data sets, we demonstrate that, in addition to decreasing the output size, our algorithm can achieve a five-fold speed up over the current state-of-the-art subgraph mining algorithms.
8256320
Fast computation with neural oscillators
This paper studies new spike-based models for winner-take-all computation and coincidence detection. In both cases, fast convergence is achieved independent of initial conditions, and network complexity is linear in the number of inputs. Fully distributed versions can be modelled based on groups of interneurons connected through electrical synapses.
385307
STING: A Statistical Information Grid Approach to Spatial Data Mining
Spatial data mining, i.e., discovery of interesting characteristics and patterns that may implicitly exist in spatial databases, is a challenging task due to the huge amounts of spatial data and to the new conceptual nature of the problems which must account for spatial distance. Clustering and region oriented queries are common problems in this domain. Several approaches have been presented in recent years, all of which require at least one scan of all individual objects (points). Consequently, the computational complexity is at least linearly proportional to the number of objects to answer each query. In this paper, we propose a hierarchical statistical information grid based approach for spatial data mining to reduce the cost further. The idea is to capture statistical information associated with spatial cells in such a manner that whole classes of queries and clustering problems can be answered without recourse to the individual objects. In theory, and confirmed by empirical studies, this approach outperforms the best previous method by at least an order of magnitude, especially when the data set is very large.
20701407
A General Structure of Feedback Shift Registers for Built-In Self Test
A mixed-type feedback shift register (MFSR) is simi lar to a linear feedback shift register (LFSR) except that the connection between two consecutive flip-flops (F/F's) may be through the Q or output, and an extra inver ter may exist at the input to the first flip-flop (stage) of the register. In this p aper, we exploit the properties of MFSR's and show that by using an MFSR based pseudorandom pattern generator (PRPG) or multiple input signature analyzer (MISA), several good features for built-in self test can be obtained. Specifically w e show that: (1) for any given initial seed, an MFSR always exists that can generate the s ame serial output sequence as can an LFSR with the same characteristic polynomial and any initial seed; (2) for any MFSR, we can always find an initial seed for this M FSR such that it can generate the same serial output sequence as can an LFSR with the same characteristic polynomial and any initial seed; and (3) for any given initial seed and any test response to be compressed, an MFSR based MISA can usually be found that will result in any required final signature. If such an MFSR cannot b e found for a specific initial seed and a specific test response sequence, we show that by simply adding one arbitrary dummy pattern to the test response, one can always find the required MFSR. We also show that if the characteristic polynomial of the MFSR based MISA can be chosen freely, it is almost guaranteed that a feasi ble MFSR can be found without adding any dummy patterns to the test response. Fo r example, for a 16-stage MISA, the probability that a feasible MFSR does not exist is less than 2-32768.
28890
Extension of Lower Probabilities and Coherence of Belief Measures
Coherence is an important concept which is introduced and discussed in a new mathematics branch, Imprecise Probability Theory. By using the Choquet integral, belief measures can be extended to be coherent lower previsions on the linear space consisting of all bounded functions. As a special case, we establish that all belief measures are coherent imprecise probabilities.