37647794
On 3-colorable plane graphs without 5- and 7-cycles
In this note, it is proved that every plane graph without 5- and 7-cycles and without adjacent triangles is 3-colorable. This improves the result of [O.V. Borodin, A.N. Glebov, A. Raspaud, M.R. Salavatipour, Planar graphs without cycles of length from 4 to 7 are 3-colorable, J. Combin. Theory Ser. B 93 (2005) 303-311], and offers a partial solution for a conjecture of Borodin and Raspaud [O.V. Borodin, A. Raspaud, A sufficient condition for planar graphs to be 3-colorable, J. Combin. Theory Ser. B 88 (2003) 17-27].
20988039
Two conjectures equivalent to the perfect graph conjecture
Abstract In this note, we study the graphs with the property that each of their induced subgraphs has circular clique number (defined in Section 2) the same as its clique number, prove that a graph satisfies such a property if and only if neither itself nor its complement contains an induced subgraph isomorphic to an odd cycle of length at least five, and then give two conjectures which are equivalent to the perfect graph conjecture.
11402970
On structure of graphs embedded on surfaces of nonnegative characteristic with application to choosability
In this paper, we prove a structural theorem of Lebesgue's type concerning some unavoidable configurations for graphs which can be embedded on surfaces of nonnegative characteristic and in which no two 3-cycles share a common vertex. As a corollary, we get a result about choosability of graphs embedded in surface of positive characteristic.
16379968
On Structure of Some Plane Graphs with Application to Choosability
A graph G=(V, E) is (x, y)-choosable for integers xy?1 if for any given family {A(v)?v?V} of sets A(v) of cardinality x, there exists a collection {B(v)?v?V} of subsets B(v)?A(v) of cardinality y such that B(u)?B(v)=? whenever uv?E(G). In this paper, structures of some plane graphs, including plane graphs with minimum degree 4, are studied. Using these results, we may show that if G is free of k-cycles for some k?{3, 4, 5, 6}, or if any two triangles in G have distance at least 2, then G is (4m, m)-choosable for all nonnegative integers m. When m=1, (4m, m)-choosable is simply 4-choosable. So these conditions are also sufficient for a plane graph to be 4-choosable.
30641096
On the fixed edge of planar graphs with minimum degree five
Abstract An edge e of a finite and simple graph G is called a fixed edge of G if G - e + e ′ ≅ G implies e ′ = e . In this paper, we show that planar graphs with minimum degree 5 contain fixed edges, from which we prove that a class of planar graphs with minimum degree one is edge reconstructible.
8227025
A Browser Compatibility Testing Method Based on Combinatorial Testing
For ensuring the displaying effects of Web applications, it is important to perform compatibility testing for browsers under the different configurations and it is a hard task to test all. So this paper focused on the improvements for browser compatibility testing. Firstly, we introduced the related work. Then we analysed the functional speciality of the current popular browsers, and provided the preconditions to simplify problems. Next we gave an instance and brought forward the single factor covering method and the pair-wise covering design to gain testing suits. Finally, we introduced the assistant tools we have developed and the future work.
38400231
On mixed Ramsey numbers
Abstract For a graph theoretic parameter f , an integer m and a graph H , the mixed Ramsey number v(f; m; H) is defined as the least positive integer p such that if G is any graph of order p , then either f(G) ⩾ m or Ḡ contains a subgraph isomorphic to H . Let ϱ denote vertex linear arboricity and let H be any connected graph of order n . In this note we show that v(ϱ; m; H) = 1 + (n + n p ( H ) − 2)(m − 1) , where n p ( H ) is the path partition number of H .
32570723
Parallel algorithm for mining fuzzy association rules
The principle and steps of the algorithm for mining fuzzy association rules is studied, and the parallel algorithm for mining fuzzy association rules is presented. In this parallel mining algorithm, quantitative attributes are partitioned into several fuzzy sets by the parallel fuzzy c-means algorithm, and fuzzy sets are applied to soften the partition boundary of the attributes. Then, the parallel algorithm for mining Boolean association rules is improved to discover frequent fuzzy attributes. Last, the fuzzy association rules with at least fuzzy confidence are generated on all processors. The parallel mining algorithm is implemented on the distributed linked PC/workstation. The experiment results show that the parallel mining algorithm has fine scaleup, sizeup and speedup.
5196479
Odd Wheels in Graphs
For k?1 the odd wheel of 2k+1 spokes, denoted by W2k+1, is the graph obtained from a cycle of length 2k+1 by adding a new vertex and joining it to all vertices of the cycle. In this paper it is shown that if a graph G of order n with minimum degree greater than 7n/12 is at least 4-chromatic then G contains an odd wheel with at most 5 spokes.
31788400
Extremal graphs for inequalities involving domination parameters
Abstract A characterization of n-vertex isolate-free connected graphs G whose domination number γ ( G ) satisfies γ(G)=⌊n/2⌋ is obtained. This result enables us to obtain extremal graphs of inequalities which bound the sum of two domination parameters in isolate-free graphs.