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Avoidable paths in graphs
[article]

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. ...

##
###
Avoidable Paths in Graphs

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. ...

##
###
Finding paths in graphs avoiding forbidden transitions

2003
*
Discrete Applied Mathematics
*

We study the computational complexity of finding T -compatible

doi:10.1016/s0166-218x(02)00251-2
fatcat:k437uzgksva53gzzz6oghhghte
*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*...##
###
Generating Avoidance Motion Using Motion Graph
[chapter]

2011
*
Lecture Notes in Computer Science
*

To realize such

doi:10.1007/978-3-642-25090-3_11
fatcat:2psizij4brbx7h3sks5inuooga
*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. ...##
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Computing and Listing Avoidable Vertices and Paths
[article]

2022
*
arXiv
*
pre-print

The notion of

arXiv:2108.07160v2
fatcat:dgt47zwrrfbstece2b7hw7ngwe
*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. ...##
###
Shifting paths to avoidable ones
[article]

2021
*
arXiv
*
pre-print

An induced

arXiv:2008.01128v2
fatcat:ekj7os2gbndihoo7bxy4k7szou
*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). ...##
###
Multi-agent Optimal Path Planning for Mobile Robots in Environment with Obstacles
[chapter]

2000
*
Lecture Notes in Computer Science
*

New algorithm applies changes of robots'

doi:10.1007/3-540-46562-6_45
fatcat:vrvoqndfv5h6pjuyhuvpjyuwsa
*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. ...##
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Near Optimal Algorithm for Fault Tolerant Distance Oracle and Single Source Replacement Path problem
[article]

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). ...

##
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Highly nonconcurrent longest paths and cycles in lattices

2014
*
Turkish Journal of Mathematics
*

Gallai [2] raised the following question

doi:10.3906/mat-1302-44
fatcat:hwefyjv4wbb4fiqc7izouw52iy
*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 . ...##
###
Complexity of the Steiner Network Problem with Respect to the Number of Terminals

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

doi:10.4230/lipics.stacs.2019.25
dblp:conf/stacs/EibenKPS19
fatcat:7gtnehfmnzh6noarhqrvg7zu6i
*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*. ...##
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Mixed fault diameter of Cartesian graph bundles II

2015
*
Ars Mathematica Contemporanea
*

A

doi:10.26493/1855-3974.390.1c5
fatcat:elpxnfqu3fbflirrsm6kfxuesm
*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 = ∅. ...##
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Avoidability beyond paths
[article]

2022
*
arXiv
*
pre-print

The concept of

arXiv:2208.12803v1
fatcat:5r73ddbopnhr5ee7nhi3ceylte
*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. ...##
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Redundancy Avoiding Algorithm in Network

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. ...

##
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A Two-Connected Graph with Gallai's Property

2019
*
Advances in Wireless Communications and Networks
*

Before the discovery of Hypo-traceable

doi:10.11648/j.awcn.20190501.14
fatcat:cems36b3e5d3jjlugdxp4htjqi
*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*. ...##
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Developing Dijik-Primbert Algorithm for Finding Unpredictable Paths over Time-Varying Networks

2016
*
Circuits and Systems
*

Communication is processed

doi:10.4236/cs.2016.711301
fatcat:ydaqtmzgofcy7h7vbi7ww2yy2q
*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. ...
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