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Avoidable paths in graphs [article]

Marthe Bonamy and Oscar Defrain and Meike Hatzel and Jocelyn Thiebaut
2019 arXiv   pre-print
In the line of previous works, we discuss conditions for multiple avoidable paths to exist.  ...  Avoidability generalises the notion of simpliciality best known in the context of chordal graphs.  ...  We are indebted to Michał Pilipczuk for providing helpful references regarding the complexity of finding an induced path of given length.  ... 
arXiv:1908.03788v1 fatcat:vyldpisxcjgmhppfchicn7svwq

Avoidable Paths in Graphs

Marthe Bonamy, Oscar Defrain, Meike Hatzel, Jocelyn Thiebaut
2020 Electronic Journal of Combinatorics  
In the line of previous works, we discuss conditions for multiple avoidable paths to exist.  ...  Avoidability generalises the notion of simpliciality best known in the context of chordal graphs.  ...  We are indebted to Micha l Pilipczuk for providing helpful references regarding the complexity of finding an induced path of given length.  ... 
doi:10.37236/9030 fatcat:dova7wywhretnjonxjg735oqxe

Finding paths in graphs avoiding forbidden transitions

Stefan Szeider
2003 Discrete Applied Mathematics  
We study the computational complexity of finding T -compatible paths between two given vertices of a graph for a specified transition system T ⊆ A.  ...  We consider graphs G with prescribed transition pair uv, vw of consecutive edges of P form an edge in T (v). Let A be a given class of graphs (closed under isomorphism).  ...  In its proof we use an intermediary reduction of 3-SAT (which is well-known to be NP-complete, see e.g., [9] ) to the problem of finding paths in graphs avoiding forbidden pairs of vertices (i.e., paths  ... 
doi:10.1016/s0166-218x(02)00251-2 fatcat:k437uzgksva53gzzz6oghhghte

Generating Avoidance Motion Using Motion Graph [chapter]

Masaki Oshita, Naoki Masaoka
2011 Lecture Notes in Computer Science  
To realize such avoidance motion, we developed criteria to find an appropriate path (series of edges) in the motion graph.  ...  We propose a method of generating avoidance motions. We use a motion graph to generate continuous motions, including both avoidance and other kinds of motions.  ...  Conclusion We presented a method of generating avoidance motions using a motion graph. We proposed new criteria based on attack, avoidance and body space-time volumes.  ... 
doi:10.1007/978-3-642-25090-3_11 fatcat:2psizij4brbx7h3sks5inuooga

Computing and Listing Avoidable Vertices and Paths [article]

Charis Papadopoulos, Athanasios Zisis
2022 arXiv   pre-print
The notion of avoidable vertices generalizes the concept of simplicial vertices in the following way: a vertex u is avoidable if every induced path on three vertices with middle vertex u is contained in  ...  To complement our results, we consider their natural generalizations of avoidable edges and avoidable paths.  ...  Let P k be an induced path on k vertices of a graph G with k ≥ 3 having endpoints x and y. Then P k is an avoidable path in G if and only if xy is an avoidable edge in G+xy −I[P k ]. Proof.  ... 
arXiv:2108.07160v2 fatcat:dgt47zwrrfbstece2b7hw7ngwe

Shifting paths to avoidable ones [article]

Vladimir Gurvich, Matjaž Krnc, Martin Milanič, Mikhail Vyalyi
2021 arXiv   pre-print
An induced path in a graph is said to be avoidable if each of its extensions is contained in an induced cycle.  ...  An extension of an induced path P in a graph G is an induced path P' such that deleting the endpoints of P' results in P.  ...  The work for this paper was done in the framework of a bilateral project between Slovenia and Russia, financed by the Slovenian Research Agency (BI-RU/19-20-022).  ... 
arXiv:2008.01128v2 fatcat:ekj7os2gbndihoo7bxy4k7szou

Multi-agent Optimal Path Planning for Mobile Robots in Environment with Obstacles [chapter]

Fedor A. Kolushev, Alexander A. Bogdanov
2000 Lecture Notes in Computer Science  
New algorithm applies changes of robots' paths and speeds to avoid collisions in multi-agent environment.  ...  When planning the path of each robot, the graph model of environment is dynamically changed for path correction and collision avoidance.  ...  -The graph (in particular, weights of the edges) can be changed, when planning a path of each robot to avoid collisions.  ... 
doi:10.1007/3-540-46562-6_45 fatcat:vrvoqndfv5h6pjuyhuvpjyuwsa

Near Optimal Algorithm for Fault Tolerant Distance Oracle and Single Source Replacement Path problem [article]

Dipan Dey, Manoj Gupta
2022 arXiv   pre-print
In a graph G with a source s, we design a distance oracle that can answer the following query: Query(s,t,e) – find the length of shortest path from a fixed source s to any destination vertex t while avoiding  ...  Using our distance oracle, we also solve the single source replacement path problem (SSR problem).  ...  Again, by Lemma 5.3, all the candidate departing paths avoiding edges in sp path avoid p too. But by Lemma 5.2, the number of such paths is O( n).  ... 
arXiv:2206.15016v1 fatcat:4zv4gyxvk5hyhhixom5l2t4rvm

Highly nonconcurrent longest paths and cycles in lattices

2014 Turkish Journal of Mathematics  
Gallai [2] raised the following question in 1966. Do there exist connected graphs such that for any vertex there exists some longest path avoiding it?  ...  The longest paths of the first type avoid a whole copy of H not containing any end-points (i.e. x, y , or z ), while the longest paths of the second type avoid a whole copy of H containing exactly one  ...  An embedding of the graph G(0, 5) in L 4 is shown in Figure 16 . This is done by using again the embedding of the graph H shown in Figure 9 .  ... 
doi:10.3906/mat-1302-44 fatcat:hwefyjv4wbb4fiqc7izouw52iy

Complexity of the Steiner Network Problem with Respect to the Number of Terminals

Eduard Eiben, Dusan Knop, Fahad Panolan, Ondrej Suchý, Michael Wagner
2019 Symposium on Theoretical Aspects of Computer Science  
Our task is to output a subgraph H ⊆ G of the minimum cost such that there is a directed path from s to t in H for all st ∈ A(R).  ...  In the Directed Steiner Network problem we are given an arc-weighted digraph G, a set of terminals T ⊆ V (G) with |T | = q, and an (unweighted) directed request graph R with V (R) = T .  ...  Let W be a set of vertices, we say that a path Q is a W -avoiding path if Q ∩ W = ∅; if P is a path we say that Q is P -avoiding path if it is a V (P )-avoiding path.  ... 
doi:10.4230/lipics.stacs.2019.25 dblp:conf/stacs/EibenKPS19 fatcat:7gtnehfmnzh6noarhqrvg7zu6i

Mixed fault diameter of Cartesian graph bundles II

Rija Erveš, Janez Žerovnik
2015 Ars Mathematica Contemporanea  
A graph is (p, q)+connected if it remains connected after removal of any p vertices and any q edges. Let F be a connected graph with the diameter D(F ) > 1, and B be (p, q)+connected graph.  ...  Upper bounds for the mixed fault diameter of Cartesian graph bundle G with fibre F over the base graph B are given.  ...  Let G be a graph and X ⊆ S(G) be a set of elements of G. A path P from a vertex x to a vertex y avoids X in G, if S(P ) ∩ X = ∅, and it internally avoids X, if (S(P ) \ {x, y}) ∩ X = ∅.  ... 
doi:10.26493/1855-3974.390.1c5 fatcat:elpxnfqu3fbflirrsm6kfxuesm

Avoidability beyond paths [article]

Vladimir Gurvich, Matjaž Krnc, Martin Milanič, Mikhail Vyalyi
2022 arXiv   pre-print
The concept of avoidable paths in graphs was introduced by Beisegel, Chudnovsky, Gurvich, Milanič, and Servatius in 2019 as a common generalization of avoidable vertices and simplicial paths.  ...  In 2020, Bonamy, Defrain, Hatzel, and Thiebaut proved that every graph containing an induced path of order k also contains an avoidable induced path of the same order.  ...  The fourth author was supported in part by the state assignment topic no. 0063-2016-0003 and RFBR grant no 20-01-00645.  ... 
arXiv:2208.12803v1 fatcat:5r73ddbopnhr5ee7nhi3ceylte

Redundancy Avoiding Algorithm in Network

Sanjeev Gangwar, Department of Computer Application, VBS Purvanchal University Jaunpur (U.P.), India, Santosh Kumar Yadav, Ashok Kumar Yadav
2018 Journal of clean energy technologies  
In which easily finds the cycle in a network or not. If a cycle between switch devices so need to remove the cycle.  ...  For finding more reliable, we need two or more paths between switches. Multiple path between two system is insure that more reliable.  ...  Fig. 3 . 3 Problem in redundant path. Fig. 4 . 4 Avoid redundancy.  ... 
doi:10.7763/ijcte.2018.v10.1207 fatcat:uwvaztaegfexfec67c5dq2gli4

A Two-Connected Graph with Gallai's Property

Abdul Naeem Kalhoro, Ali Dino Jumani
2019 Advances in Wireless Communications and Networks  
Before the discovery of Hypo-traceable graphs, Tibor Gallai, in 1966, raised the question whether the graphs in which each vertex is missed by some longest path.  ...  that whether there exists graphs of Paths and Cycles, that is to say i-connected graphs (planar or non-planar respectively), such that each set of j points are disjoint from some longest paths or cycles  ...  A path that also visit through every vertex once with no recurrences, and it does not have to start and end at the similar vertex in a graph is said to be Hamiltonian path.  ... 
doi:10.11648/j.awcn.20190501.14 fatcat:cems36b3e5d3jjlugdxp4htjqi

Developing Dijik-Primbert Algorithm for Finding Unpredictable Paths over Time-Varying Networks

P. Sushmitha, R. Kanthavel
2016 Circuits and Systems  
Communication is processed in unpredictable paths by the use of path following and directed communication graph.  ...  Primloyd algorithm is used for finding shortest paths in a weighted undirected graph for conquering the complexity in matrix coding.  ...  Dijikloyd algorithm is a graph search algorithm for finding shortest paths in a weighted directed graph with positive and negative edge weights.  ... 
doi:10.4236/cs.2016.711301 fatcat:ydaqtmzgofcy7h7vbi7ww2yy2q
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