we study the problem of finding a maximum clique in the visibility graph of a simple polygon withnvertices. We show that this problem is very hard, if the input polygons are allowed to contain holes: a gap-preserving reduction from the maxi-mum clique problem on general ...
Stamm, Maximum clique and minimum clique partition in visibility graphs, in: Proceeding of IFIP TCS, in: Lecture Notes in Computer Science, vol. 1872, Springer-Verlag, 2000, pp. 200-212.S. Eidenbenz and C. Stamm. Maximum clique and minimum clique partition in visibility graphs. In TCS '...
In an alternative approach to "characterizing" the graph class of visibility graphs of simple polygons, we study the problem of finding a maximum clique in the visibility graph of a simple polygon with n vertices. We show that this problem is very hard, if the input polygons are allowed to...
State-of-the-art branch-and-bound algorithms for the maximum clique problem (Maxclique) frequently use an upper bound based on a partition P of a graph into independent sets for a maximum clique of the graph, which cannot be very tight for imperfect graphs. In this paper we propose a new...
A (vertex) k-colouring of a graph G, which we denote Ck(G), is a partition of V(G) into k independent sets; precisely: Ck(G)={I1,I2,…,Ik}. Clearly, χ(G) provides an upper bound on the clique number ω(G), see, e.g., Balas & Yu (1986), and, consequently, so is...
We will show that the problem Partition into Subgraphs Isomorphic toP3 is NP-complete for bipartite graphs. Notice that this result follows from the proof given by Kirkpatrick and Hell [24], [25] on NP-completeness of the problem for general graphs. We offer another proof which can be direc...
Penev, I.: Perfect graphs with no balanced skew-partition are 2-clique-colorable. J. Graph Theory 81, 213–235 (2016) Article MathSciNet Google Scholar Shan, E., Liang, Z., Kang, L.: Clique-transversal sets and clique-coloring in planar graphs. Eur. J. Combin. 36, 367–376 (20...
The achromatic number psi(G) of a graph G = (V,E) is the maximum k such that V has a partition V1, V2,...,Vk into independent sets, the union of no pair of... RW Irving,DF Manlove - 《Discrete Applied Mathematics》 被引量: 387发表: 1999年 THE FRACTIONAL CHROMATIC NUMBER OF...
(n3) algorithm for the maximum weight clique problem for this class, where n denotes the number of vertices and m the number of edges of the input ... K Cameron,S Huang,I Penev,... - 《Journal of Graph Theory》 被引量: 0发表: 2020年 ...
where Ω denotes the sample space of the discrete-valued random vector z, Q is the partition function (normalization constant) given by (34)Q=∑ω∈Ωexp{−U(ω)} U(z) is the potential function given by (35)U(z)=∑xi∑xj∈NxiVc(z(xi),z(xj)) which can be expressed as a sum...