Konstanty Junosza-Szaniawski

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An L(2, 1)-labeling of a graph is a mapping from its vertex set into nonnegative integers such that the labels assigned to adjacent vertices differ by at least 2, and labels assigned to vertices of distance 2 are different. The span of such a labeling is the maximum label used, and the L(2, 1)-span of a graph is the minimum possible span of its L(2,(More)
In this paper we consider a variation of a recoloring problem, called the Color-Fixing. Let us have some non-proper r-coloring φ of a graph G. We investigate the problem of finding a proper r-coloring of G, which is “the most similar” to φ, i.e. the number k of vertices that have to be recolored is minimum possible. We observe that the problem is(More)
The generalized list T -coloring is a common generalization of many graph coloring models, including classical coloring, L(p, q)-labeling, channel assignment and T -coloring. Every vertex from the input graph has a list of permitted labels. Moreover, every edge has a set of forbidden differences. We ask for such a labeling of vertices of the input graph(More)
L(2, 1)-labeling is a graph coloring model inspired by a channel assignment problem in telecommunication. It asks for such a labeling of vertices with nonnegative integers that adjacent vertices get labels that di er by at least 2 and vertices in distance 2 get di erent labels. It is known that for any xed k ≥ 4 it is NP-complete to determine if a graph has(More)
Abstract. In this paper we give an algorithm for counting the number of all independent sets in a given graph which works in time O(1.1394) for subcubic graphs and in time O(1.2369) for general graphs, where n is the number of vertices in the instance graph, and polynomial space. The result comes from combining two well known methods “Divide and Conquer”(More)
We formulate general boundary conditions for a labelling to assure the existence of a balanced n-simplex in a triangulated polyhedron. Furthermore we prove a Knaster-Kuratowski-Mazurkiewicz type theorem for polyhedrons and generalize some theorems of Ichiishi and Idzik. We also formulate a necessary condition for a continuous function defined on a(More)