12925025
The 4-Choosability of Plane Graphs without 4-Cycles'
A graphGis calledk-choosable ifkis a number such that if we give lists ofkcolors to each vertex ofGthere is a vertex coloring ofGwhere each vertex receives a color from its own list no matter what the lists are. In this paper, it is shown that each plane graph without 4-cycles is 4-choosable.
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].
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.
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.
14675818
A physically based method for triangulated surface flattening
This paper introduces a new method of generating 2D flat patterns from a 3D triangulated surface by opening the bending configuration of each winged triangle pair. The flattening can be divided into four steps. First, a 3D triangulated surface is modeled with a mass-spring system that simulates the surface deformation during the flattening. Second, an unwrapping force field is built to drive the mass-spring system to a developable configuration through the numerical integration. Third, a velocity redistribution procedure is initiated to average velocity variances among the particles. Finally, the mass-spring system is forced to collide with a plane, and the final 2D pattern is generated after all the winged triangle pairs are spread onto the colliding plane. To retain the size and area of the original 3D surface, a strain control mechanism is introduced to keep the springs from over-elongation or over-shrinkage at each time step.
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.
29802636
Two classes of edge domination in graphs
Let γ's(G) (γ'l(G), resp.) be the number of (local) signed edge domination of a graph G [B. Xu, On signed edge domination numbers of graphs, Discrete Math. 239 (2001) 179-189]. In this paper, we prove mainly that γ's(G) ≤ ⌊11/6n - 1⌋ and γ's(G) ≤ 2n - 4 hold for any graph G of order n (n ≥ 4), and pose several open problems and conjectures.
30598486
Regression testing for Web applications based on slicing
Web applications have rapid developing speed and changeable user demands, so the regression testing is much important. Since the changed demands result in different versions of Web applications, and the faults usually hiding in the adjusted contents, the regression testing must cover all the related pages. In order to carry through the regression testing quickly and effectively, we make the simplification with the method of slicing. Firstly, we analyze the possible changes in the Web applications and the influences produced by these changes, discussing in the direct-dependent and indirect-dependent way; next, we give the regression testing method based on slicing emphasized on the indirect-dependent among data, i.e., obtaining the dependent set of changed variables by forward and backward search method and generating the testing suits; conclusion remarks and future work are given at last.
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.