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The problem of computing the chromatic number of a P 5-free graph (a graph which contains no path on 5 vertices as an induced subgraph) is known to be NP-hard. However, we show that for every fixed integer k, there exists a polynomial-time algorithm determining whether or not a P 5-free graph admits a k-coloring, and finding one, if it does.
Suppose that we are given two independent sets I0 and Ir of a graph such that |I0| = |Ir|, and imagine that a token is placed on each vertex in I0. The token jumping problem is to determine whether there exists a sequence of independent sets which transforms I0 into Ir so that each independent set in the sequence results from the previous one by moving(More)
We study problems of reconfigurability of independent sets in graphs. We consider three different models (token jumping, token sliding, and token addition and removal) and analyze relationships between them. We prove that independent set reconfigurability in perfect graphs (under any of the three models) generalizes the shortest path reconfigurability(More)
Vertex and edge colorability are two graph problems that are NP-hard in general. We show that both problems remain difficult even for graphs without short cycles, i.e., without cycles of length at most g for any particular value of g. On the contrary, for graphs without long cycles, both problems can be solved in polynomial time.
We study the following problem on reconguring shortest paths in graphs: Given two shortest s-t paths, what is the minimum number of steps required to transform one into the other, where each intermediate path must also be a shortest s-t path and must dier from the previous one by only one vertex. We prove that the shortest reconguration sequence can be(More)
Independent sets, induced matchings and cliques are examples of regular induced subgraphs in a graph. In this paper, we prove that finding a maximum cardinality k-regular induced subgraph is an NP-hard problem for any value of k. We propose a convex quadratic upper bound on the size of a k-regular induced subgraph and characterize those graphs for which(More)
The k-in-a-Path problem is to test whether a graph contains an induced path spanning k given vertices. This problem is NP-complete in general graphs, already when k=3. We show how to solve it in polynomial time on claw-free graphs, when k is an arbitrary fixed integer not part of the input. As a consequence, also the k-Induced Disjoint Paths and the(More)
The paper presents the application of an adaptive neural controller used for speed control of electrical drives with elastic joint. The described project is realized in CompactRIO controller (cRIO-real-time embedded controller with reconfigurable input and output modules) equipped with an FPGA chip. The proposed speed controller is based on Adaptive Linear(More)
The two-player, complete information game of Cops and Robber is played on undirected finite graphs. A number of cops and one robber are positioned on vertices and take turns in sliding along edges. The cops win if, after a move, a cop and the robber are on the same vertex. The minimum number of cops needed to catch the robber on a graph is called the cop(More)
The MIT Faculty has made this article openly available. Please share how this access benefits you. Your story matters. Abstract. We study the problem of reconfiguring one list edge-coloring of a graph into another list edge-coloring by changing only one edge color assignment at a time, while at all times maintaining a list edge-coloring, given a list of(More)