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Graph theoretic and algorithmic aspect of the equitable coloring problem in block graphs [PDF]
Discrete Mathematics & Theoretical Computer Science, 2022 An equitable coloring of a graph $G=(V,E)$ is a (proper) vertex-coloring of $G$, such that the sizes of any two color classes differ by at most one. In this paper, we consider the equitable coloring problem in block graphs.
Hanna Furmańczyk, Vahan Mkrtchyan
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A Parameterized Approximation Algorithm for the Chromatic k-Median Problem
IEEE Access, 2021 Chromatic $k$ -median is a frequently encountered problem in the determination of the topological structures of chromosomes. This problem considers a set $\mathcal {C}$ of colored clients and a set $\mathcal {F}$ of facilities located in a metric ...
Zhen Zhang, Jinchuan Zhang, Lingzhi Zhu
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Imbalance is fixed parameter tractable [PDF]
Information Processing Letters, 2010 zbMATH Open Web Interface contents unavailable due to conflicting licenses.
Daniel Lokshtanov +2 more
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Journal of Graph Algorithms and Applications, 2022 In the classical partial vertex cover problem, we are given a graph $G$ and two positive integers $k_1$ and $k_2$. The goal is to check whether there is a subset $V'$ of $V$ of size at most $k_1$, such that $V'$ covers at least $k_2$ edges of $G$.
Vahan Mkrtchyan, Garik Petrosyan
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Distortion Is Fixed Parameter Tractable [PDF]
ACM Transactions on Computation Theory, 2009 We study low-distortion embedding of metric spaces into the line, and more generally, into the shortest path metric of trees, from the parameterized complexity perspective. Let M = M ( G ) be the shortest path metric of an edge-weighted graph G ,
Michael R. Fellows +5 more
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Minimum Bisection Is Fixed-Parameter Tractable [PDF]
SIAM Journal on Computing, 2014 In the classic Minimum Bisection problem we are given as input a graph $G$ and an integer $k$. The task is to determine whether there is a partition of $V(G)$ into two parts $A$ and $B$ such that $||A|-|B|| \leq 1$ and there are at most $k$ edges with one endpoint in $A$ and the other in $B$.
Marek Cygan +4 more
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Finding Detours is Fixed-Parameter Tractable [PDF]
SIAM Journal on Discrete Mathematics, 2019 Extended abstract appears at ICALP ...
Ivona Bezáková +3 more
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On fixed-parameter tractability of the mixed domination problem for graphs with bounded tree-width [PDF]
Discrete Mathematics & Theoretical Computer Science, 2018 A mixed dominating set for a graph $G = (V,E)$ is a set $S\subseteq V \cup E$ such that every element $x \in (V \cup E) \backslash S$ is either adjacent or incident to an element of $S$. The mixed domination number of a graph $G$, denoted by $\gamma_m(G)$
M. Rajaati +3 more
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Interval Deletion Is Fixed-Parameter Tractable [PDF]
ACM Transactions on Algorithms, 2013 We study the minimum interval deletion problem, which asks for the removal of a set of at most k vertices to make a graph of n vertices into an interval graph. We present a parameterized algorithm of runtime 10 k ⋅ n
Yixin Cao 0001, Dániel Marx
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Rotation distance is fixed-parameter tractable [PDF]
Information Processing Letters, 2009 Rotation distance between trees measures the number of simple operations it takes to transform one tree into another. There are no known polynomial-time algorithms for computing rotation distance. In the case of ordered rooted trees, we show that the rotation distance between two ordered trees is fixed-parameter tractable, in the parameter, k, the ...
Sean Cleary, Katherine St. John
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