Filters








3,390 Hits in 4.5 sec

The k-in-a-Path Problem for Claw-free Graphs

Jiří Fiala, Marcin Kamiński, Bernard Lidický, Daniël Paulusma
2010 Algorithmica  
We show how to solve this problem in polynomial time on claw-free graphs, when k is not part of the input but an arbitrarily fixed integer.  ...  Testing whether there is an induced path in a graph spanning k given vertices is already NP-complete in general graphs when k=3.  ...  Acknowledgments We would like to thank the two anonymous referees for their helpful comments.  ... 
doi:10.1007/s00453-010-9468-z fatcat:76mfyeqqvrfq3jo2ucurnkggmq

THE k-IN-A-PATH PROBLEM FOR CLAW-FREE GRAPHS

Jiř´i Jiˇ, Jiř Jiř´, Jiř´i Fiala, Marcin Kami´nski, Kami´ Kami´nski, Bernard Lidick´y, Lidick´ Lidick´y, Dani¨el Dani¨, Dani¨el Paulusma
2010 Symposium on Theoretical Aspects of Computer Science   unpublished
We show how to solve this problem in polynomial time on claw-free graphs, when k is not part of the input but an arbitrarily fixed integer.  ...  Testing whether there is an induced path in a graph spanning k given vertices is already NP-complete in general graphs when k = 3.  ...  Notice that any induced tree in a claw-free graph is in fact an induced path. Observation 1.2. The k-in-a-Path and k-in-a-Tree problem are equivalent for the class of claw-free graphs. Motivation.  ... 
fatcat:6cjay7p3pbba7ag4haintyhfye

Induced Disjoint Paths in Claw-Free Graphs [chapter]

Petr A. Golovach, Daniël Paulusma, Erik Jan van Leeuwen
2012 Lecture Notes in Computer Science  
Several related problems, such as the k-in-a-Path problem, are proved to be fixed-parameter tractable for claw-free graphs as well.  ...  We show that this problem is fixed-parameter tractable for claw-free graphs when parameterized by k.  ...  We would like to thank two anonymous reviewers for their comments, which helped us improve the readability of our paper.  ... 
doi:10.1007/978-3-642-33090-2_45 fatcat:dskh3ozjpbh5lmjcptcgjb6vte

Induced Disjoint Paths in Claw-Free Graphs [article]

Petr A. Golovach and Daniel Paulusma and Erik Jan van Leeuwen
2014 arXiv   pre-print
Several related problems, such as the k-in-a-Path problem, are proven to be fixed-parameter tractable for claw-free graphs as well.  ...  We show that this problem is fixed-parameter tractable for claw-free graphs when parameterized by k.  ...  The problems k-in-a-Cycle, k-in-a-Path, and k-in-a-Tree are fixed-parameter tractable for claw-free graphs when parameterized by k. Proof. First we consider the k-in-a-Cycle problem.  ... 
arXiv:1202.4419v2 fatcat:gukgczgypzcttdbwqn4bxqswnm

Induced Disjoint Paths in Claw-Free Graphs

Petr A. Golovach, Daniël Paulusma, Erik Jan van Leeuwen
2015 SIAM Journal on Discrete Mathematics  
Several related problems, such as the k-in-a-Path problem, are proved to be fixed-parameter tractable for claw-free graphs as well.  ...  We show that this problem is fixed-parameter tractable for claw-free graphs when parameterized by k.  ...  We would like to thank two anonymous reviewers for their comments, which helped us improve the readability of our paper.  ... 
doi:10.1137/140963200 fatcat:t4rpbc6wgjfercr7dr6ogilzli

Packing 3-vertex paths in claw-free graphs and related topics

Alexander Kelmans
2011 Discrete Applied Mathematics  
Let G be a 3-connected claw-free graph, x a vertex in G, e = xy an edge in G, and P a 3-vertex path in G.  ...  A claw is a graph with four vertices and three edges incident to the same vertex. A graph is claw-free if it has no induced subgraph isomorphic to a claw. Our results include the following.  ...  (c12) We show that the -packing problem for a claw-free graph G can be reduced in polynomial time to that for a special claw-free graph K (called a cactus) with v(K ) ≤ v(G) (see 4.5 and 4.6).  ... 
doi:10.1016/j.dam.2010.05.001 fatcat:74tl7ztnxrdt3ccymbrplkpbay

Deletion to Scattered Graph Classes II – Improved FPT Algorithms for Deletion to Pairs of Graph Classes [article]

Ashwin Jacob, Diptapriyo Majumdar, Venkatesh Raman
2022 arXiv   pre-print
The problem of deletion to Π, takes as input a graph G and asks for a minimum number (or a fixed integer k) of vertices to be deleted from G so that the resulting graph belongs to Π.  ...  Recently, the study of a natural extension of the problem was initiated where we are given a finite set of hereditary graph classes, and the goal is to determine whether k vertices can be deleted from  ...  Claw-free or Triangle-Free graphs We define the problem. Claw-Free-or-Triangle-Free Deletion Input: An undirected graph G = (V, E) and an integer k.  ... 
arXiv:2201.03142v1 fatcat:h6f66ushvnft3ng3aebxx2sayy

Reconfiguring Independent Sets in Claw-Free Graphs [chapter]

Paul Bonsma, Marcin Kamiński, Marcin Wrochna
2014 Lecture Notes in Computer Science  
We present a polynomial-time algorithm that, given two independent sets in a claw-free graph G, decides whether one can be transformed into the other by a sequence of elementary steps.  ...  Each elementary step is to remove a vertex v from the current independent set S and to add a new vertex w (not in S) such that the result is again an independent set.  ...  This motivated the question asked in [11] whether for connected, claw-free and evenhole-free graph G, TS k (G) is connected.  ... 
doi:10.1007/978-3-319-08404-6_8 fatcat:ktyhlpltubeefktjedu6b7kon4

Finding Induced Paths of Given Parity in Claw-Free Graphs

Pim van 't Hof, Marcin Kamiński, Daniël Paulusma
2010 Algorithmica  
Our results imply that the problem of deciding if two specified vertices of a claw-free graph form an even pair, as well as the problem of deciding if a given claw-free graph has an even pair, can be solved  ...  Although all three problems are NP-complete in general, we show that they can be solved in O(n 5 ) time for the class of claw-free graphs.  ...  The authors would like to thank Jiří Fiala, Benjamin Lévêque, Luke Mathieson, Nicolas Trotignon and two anonymous reviewers for helpful suggestions.  ... 
doi:10.1007/s00453-010-9470-5 fatcat:emwqsmiedbfrnc4qd35kei5xki

Finding Induced Paths of Given Parity in Claw-Free Graphs [chapter]

Pim van 't Hof, Marcin Kamiński, Daniël Paulusma
2010 Lecture Notes in Computer Science  
Our results imply that the problem of deciding if two specified vertices of a claw-free graph form an even pair, as well as the problem of deciding if a given claw-free graph has an even pair, can be solved  ...  Although all three problems are NP-complete in general, we show that they can be solved in O(n 5 ) time for the class of claw-free graphs.  ...  The authors would like to thank Jiří Fiala, Benjamin Lévêque, Luke Mathieson, Nicolas Trotignon and two anonymous reviewers for helpful suggestions.  ... 
doi:10.1007/978-3-642-11409-0_30 fatcat:hstidpzhcjgvzka2vl6sd6yxma

On linear and circular structure of (claw, net)-free graphs

Andreas Brandstädt, Feodor F. Dragan
2003 Discrete Applied Mathematics  
We show also how one can use structural properties of (claw, net)-free graphs to solve e ciently the domination, independent domination, and independent set problems on these graphs. ?  ...  Moreover, using LexBFS we present a linear time algorithm which, for a given (claw, net)-free graph, ÿnds either a dominating pair or an induced doubly dominating cycle.  ...  In [22] , Hempel and Kratsch gave linear time algorithms for all three problems on the class of claw-free AT-free graphs.  ... 
doi:10.1016/s0166-218x(02)00571-1 fatcat:2pbmjgfx7zfj7hwy3cz2djmtlm

Colouring Generalized Claw-Free Graphs and Graphs of Large Girth: Bounding the Diameter [article]

Barnaby Martin and Daniel Paulusma and Siani Smith
2021 arXiv   pre-print
A graph G is H-free if G does not contain H as an induced subgraph. It is known that for all k≥ 3, the k-Colouring problem is NP-complete for H-free graphs if H contains an induced claw or cycle.  ...  For a fixed integer, the k-Colouring problem is to decide if the vertices of a graph can be coloured with at most k colours for an integer k, such that no two adjacent vertices are coloured alike.  ...  What are the complexities of 3-Colouring for K 1 1,4 -free graphs of diameter 3 and for K 2 1,3 -free graphs of diameter 3? Open Problem 4.  ... 
arXiv:2111.11897v1 fatcat:w76s7sr3oze47fuxugd5767g4i

Intersection Graphs of Non-crossing Paths [article]

Steven Chaplick
2020 arXiv   pre-print
A direct consequence of our certifying algorithms is a linear time algorithm certifying the presence/absence of an induced claw (K_1,3) in a chordal graph.  ...  For the intersection graphs of NC paths of a tree, we characterize the minimum connected dominating sets (leading to a linear time algorithm to compute one).  ...  This is relevant for us because, as we will see in Section 3, the claw-free chordal graphs are precisely the NC-path-tree graphs.  ... 
arXiv:1907.00272v2 fatcat:paeipvyuk5gmxl6wcunfatj56a

On the Erdős-Gyárfás conjecture in claw-free graphs [article]

Pouria Salehi Nowbandegani, Hossein Esfandiari, Mohammad Hassan Shirdareh Haghighi, Khodakhast Bibak
2013 arXiv   pre-print
In this paper, we obtain some results on this question, in particular for cubic claw-free graphs.  ...  Since this conjecture has proven to be far from reach, Hobbs asked if the Erdős-Gyárfás conjecture holds in claw-free graphs.  ...  In the last section, we discuss on the conjecture in cubic claw-free graphs. We also pose a related conjecture and a problem.  ... 
arXiv:1109.5398v3 fatcat:u5vut7kttbar7pakkg7zktj7bu

From matchings to independent sets

Vadim Lozin
2017 Discrete Applied Mathematics  
It is well-known that finding a maximum matching in G is equivalent to finding a maximum independent set in the line graph of G. For general graphs, the maximum independent set problem is NP-hard.  ...  We also review various techniques that may lead to efficient algorithms for the maximum independent set problem in restricted graph families, with a focus given to augmenting graphs and graph transformations  ...  For the same reason, paths with an even number of vertices cannot be augmenting. Therefore, every connected claw-free augmenting graph is a path P k with odd k.  ... 
doi:10.1016/j.dam.2016.04.012 fatcat:vf4xsf7is5fxni5ullpnngptqq
« Previous Showing results 1 — 15 out of 3,390 results