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Graph isomorphism is in the low hierarchy

1988
*
Journal of computer and system sciences (Print)
*

It

doi:10.1016/0022-0000(88)90010-4
fatcat:4l6j2onzijbslnow4v6g34m3mu
*is*shown that the*graph**isomorphism*problem*is*located in level L$ of the low hierarchy in*NP*. ... This implies that this problem*is*not*NP*-*complete*(even under weaker forms of polynomial reducibilities, like y-reducibility) unless the polynomial-time hierarchy collapses to some finite level. ... The*graph**isomorphism*problem*is*given as the set*GRAPH**ISOMORPHISM*= ((G,, G,) 1 G, and G, are*isomorphic*} which*is*easily seen to belong to the class*NP*, but*is*currently not known to be*NP*-*complete*...##
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Isomorphic Subgraphs
[chapter]

1999
*
Lecture Notes in Computer Science
*

We show that the

doi:10.1007/3-540-46648-7_30
fatcat:wiec3yfyk5agpeweik3zz3ybby
*Isomorphic*Subgraphs problem*is**NP*-hard for connected outerplanar*graphs*, and*2*-connected planar*graphs*and*is*solvable in linear time when restricted to trees. ... There are many*NP*-*complete*or open problems related to our problem, like*Graph**Isomorphism*,*Graph*Automorphism or Largest Common Subgraph. ... Brandenburg for his various and detailed comments and suggestions, particularly on the proof of*Isomorphic*Subgraphs of general*graphs*. ...##
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Page 662 of Mathematical Reviews Vol. , Issue 95b
[page]

1995
*
Mathematical Reviews
*

ISBN 0-8176-3680-3
The

*graph**isomorphism*problem has received much recent atten- tion. It*is*known that if P does not equal*NP*then there must exist problems that are neither*NP*-*complete*nor in P. ... The authors derive from the interactive proof theory 05 COMBINATORICS 662 the fact that if the*graph**isomorphism*problem*is**NP*-*complete*, then the polynomial-time hierarchy collapses. ...##
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Subgraph isomorphism in graph classes

2012
*
Discrete Mathematics
*

We investigate the computational complexity of the following restricted variant of Subgraph

doi:10.1016/j.disc.2012.07.010
fatcat:cxupp725szgvbj5htfpuc6vuba
*Isomorphism*: given a pair of connected*graphs*G = ... Part of this research*is*supported by the Funding Program for World-Leading Innovative R & D on Science and Technology, Japan, and Grants-in-Aid for Scientific Research from Ministry of Education, Science ... Spanning Subgraph*Isomorphism**is**NP*-*complete*even for bipartite*graphs*and for chordal*graphs*, since Hamiltonian Path on these classes*is**NP*-*complete*[10, 1] . ...##
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Square-Root Finding Problem In Graphs, A Complete Dichotomy Theorem
[article]

2012
*
arXiv
*
pre-print

Determining if a given

arXiv:1210.7684v1
fatcat:75g3etssonfa5e3gpqgl4itqna
*graph*G*is*the square of some*graph**is*not easy in general. Motwani and Sudan proved that it*is**NP*-*complete*to determine if a given*graph*G*is*the square of some*graph*. ... We introduce a family of*graphs*with exponentially many non-*isomorphic*square roots, and as the main result of this paper we prove that the square root finding problem*is**NP*-*complete*for square roots of ... r for r = 2k + 1*is**NP*-*complete*. ...##
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Induced Subtrees in Interval Graphs
[chapter]

2013
*
Lecture Notes in Computer Science
*

This problem

doi:10.1007/978-3-642-45278-9_20
fatcat:yddoddstejeohk5nb4v3zc5uvu
*is*known to be*NP*-*complete*on bipartite*graphs*, but it can be solved in polynomial time when G*is*a forest. ... In contrast to this positive result, we show that the closely related Subtree*Isomorphism*problem*is**NP*-*complete*even when G*is*restricted to the class of proper interval*graphs*, a well-known subclass ... Note that the problem*is**NP*-*complete*on perfect*graphs*, a superclass of chordal*graphs*, due to the aforementioned*NP*-*completeness*of Induced Subtree*Isomorphism*on bipartite*graphs*[7] . ...##
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Page 3786 of Mathematical Reviews Vol. , Issue 84i
[page]

1984
*
Mathematical Reviews
*

It

*is*shown that for many very simple undirected*graphs*G this question*is**NP*-*complete*(this was previously known for the*graphs*K,, only). ... Inform. and Control 51 (1981), no.*2*, 128-145. Authors’ summary: “A*graph*H*is*called an interpretation of a*graph*G if a morphic image of H*is*(*isomorphic*to) a subgraph of G. ...##
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The complexity of comparing reaction systems

2002
*
Bioinformatics
*

We show that comparing the stoichiometric structure of two reactions systems

doi:10.1093/bioinformatics/18.3.465
pmid:11934746
fatcat:tatwnrca6ndhjgj2hvfvihpqqa
*is*equivalent to the*graph**isomorphism*problem. ... The analogous problem of searching for a subsystem of a reaction system*is**NP*-*complete*. We also discuss heuristic issues in implementations for practical comparison of stoichiometric matrices. ... Matrix*isomorphism**is*reducible to*graph**isomorphism*and therefore*is*GI-*complete*. We have mentioned that submatrix*isomorphism**is**NP*-*complete*. ...##
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The Subgraph Bisimulation Problem

2003
*
IEEE Transactions on Knowledge and Data Engineering
*

We study the complexity of the Subgraph Bisimulation Problem, which stands to

doi:10.1109/tkde.2003.1209024
fatcat:vmw6gqlyizdq7jhfu64pv3kxfi
*Graph*Bisimulation as Subgraph*Isomorphism*stands to*Graph**Isomorphism*and we prove its*NP*-*Completeness*. ... Our analysis*is*motivated by its applications to Semistructured Databases. ... Each Hamilton path on a 5-nodes*graph**is**isomorphic*(hence, bisimilar) to the 5-chain C 5 . Theorem 1: The Subgraph Bisimulation problem*is**NP*-*complete*. ...##
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The complexity of Boolean matrix root computation

2004
*
Theoretical Computer Science
*

related to subdivision digraphs, root finding

doi:10.1016/j.tcs.2004.02.041
fatcat:t56g4mzfezhepofgd3ix7m3pau
*is*of the same complexity as the*graph*-*isomorphism*problem. ... Interpreting Boolean matrices as directed*graphs*, we further reveal a connection between Boolean matrix roots and*graph**isomorphism*, which leads to a proof that for a certain subclass of Boolean matrices ... for*graphs**is**NP*-*complete*[5] . ...##
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The Complexity of Boolean Matrix Root Computation
[chapter]

2003
*
Lecture Notes in Computer Science
*

related to subdivision digraphs, root finding

doi:10.1007/3-540-45071-8_23
fatcat:qhcl7kreuvg3vkotbbskjnhfpy
*is*of the same complexity as the*graph*-*isomorphism*problem. ... Interpreting Boolean matrices as directed*graphs*, we further reveal a connection between Boolean matrix roots and*graph**isomorphism*, which leads to a proof that for a certain subclass of Boolean matrices ... for*graphs**is**NP*-*complete*[5] . ...##
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On the complexity of deciding whether the distinguishing chromatic number of a graph is at most two

2011
*
Discrete Mathematics
*

We consider the problem when k =

doi:10.1016/j.disc.2010.12.013
fatcat:5e2rkmi4v5axniblk5dyzehwsy
*2*. In regards to the issue of solvability in polynomial time, we show that the problem*is*at least as hard as*graph*automorphism, but no harder than*graph**isomorphism*. ... In an article Cheng (2009) [3] published recently in this journal, it was shown that when k ≥ 3, the problem of deciding whether the distinguishing chromatic number of a*graph**is*at most k*is**NP*-hard. ...*Graph*automorphism and*graph**isomorphism*Consider the following decision problems each of which*is*known to be in*NP*, but neither of which*is*known to be in P or*NP*-*complete*. ...##
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A note on contracting claw-free graphs

2013
*
Discrete Mathematics & Theoretical Computer Science
*

We show that these problems stay

doi:10.46298/dmtcs.605
fatcat:hrmcp2vu7jehnm432miqaeucam
*NP*-*complete*even when the host and target belong to the class of line*graphs*, which form a subclass of the class of claw-free*graphs*, i.e.,*graphs*with no induced 4-vertex ... A natural question*is*to study the computational complexity of these problems if the target*graph**is*assumed to be fixed. ... Because DISSOLUTION*is**NP*-*complete*, we then find that this problem stays*NP*-*complete*even when both the host and target*graph*are line*graphs*. We now consider the*GRAPH**ISOMORPHISM*problem. ...##
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The complexity of equivalence and isomorphism of systems of equations over finite groups

2005
*
Theoretical Computer Science
*

If the group

doi:10.1016/j.tcs.2005.07.018
fatcat:63za63ve5rhsrhidxnz7b4xwbq
*is*Abelian, then the*isomorphism*problem*is**GRAPH**ISOMORPHISM*-hard. ... We show that the equivalence problem*is*in P if the group*is*Abelian, and coNP-*complete*if the group*is*non-Abelian. ... problem*is**GRAPH**ISOMORPHISM*-*complete*. ...##
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Isomorphic Implication
[article]

2005
*
arXiv
*
pre-print

We prove that, depending on the set of constraints, this problem

arXiv:cs/0412062v2
fatcat:zf326f3lj5cjtl6h5zwnwu6t7u
*is*in P,*NP*-*complete*, or*NP*-hard, coNP-hard, and in parallel access to*NP*. ... We study the*isomorphic*implication problem for Boolean constraints. We show that this*is*a natural analog of the subgraph*isomorphism*problem. ... The subgraph*isomorphism*problem for*graphs*without isolated vertices*is**NP*-*complete*. ...
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