Finding and listing induced paths and cycles

Hoíng, Chınh T.; Kamiński, Marcin; Sawada, Joe; Sritharan, R.

doi:10.1016/j.dam.2012.01.024

Cited by 12 publications

(5 citation statements)

References 10 publications

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“…More precisely, we determined for each simulated RBMG the connected components of its restrictions to any three distinct colors and determined whether these components are cographs, graphs of Type (B), or graphs of Type (C). In order to identify these graph types, we used algorithms of [Hoàngm et al, 2013] to first identify an induced P 4 belonging to a good quartet. If one exists, we check for the existence of an induced P 5 and then test whether its endpoints are connected, thus forming a hexagon characteristic for the a Type (C) graph.…”

Section: Simulation Results For Duplication/loss Scenariosmentioning

confidence: 99%

Best match graphs and reconciliation of gene trees with species trees

et al. 2020

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A wide variety of problems in computational biology, most notably the assessment of orthology, are solved with the help of reciprocal best matches. Using an evolutionary definition of best matches that captures the intuition behind the concept we clarify rigorously the relationships between reciprocal best matches, orthology, and evolutionary events under the assumption of duplication/loss scenarios. We show that the orthology graph is a subgraph of the reciprocal best match graph (RBMG). We furthermore give conditions under which an RBMG that is a cograph identifies the correct orthlogy relation. Using computer simulations we find that most false positive orthology assignments can be identified as so-called good quartets -and thus corrected -in the absence of horizontal transfer. Horizontal transfer, however, may introduce also false-negative orthology assignments.

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Section: Simulation Results For Duplication/loss Scenariosmentioning

confidence: 99%

Best match graphs and reconciliation of gene trees with species trees

et al. 2020

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“…We obtain also the following corollary from Theorem 3.6 confirming in part the upper bounds from [11,23].…”

Section: Applications To Pattern Graphs On At Most Six Verticesmentioning

confidence: 80%

Detecting and Counting Small Pattern Graphs

Floderus¹,

Kowaluk²,

Lingas³

et al. 2015

SIAM J. Discrete Math.

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We study the induced subgraph isomorphism problem and the general subgraph isomorphism problem for small pattern graphs. We present a new general method for detecting induced subgraphs of a host graph isomorphic to a fixed pattern graph by reduction to polynomial testing for nonidentity with zero over a field of finite characteristic. It yields new upper time bounds for several pattern graphs on five vertices and provides an alternative combinatorial method for the majority of pattern graphs on four and three vertices. Since our method avoids the large overhead of fast matrix multiplication, it can be of practical interest even for larger pattern graphs. Next, we derive new upper time bounds on counting the number of isomorphisms between a fixed pattern graph with an independent set of size s and a subgraph of the host graph. We also consider a weighted version of the counting problem, when one counts the number of isomorphisms between the pattern graph and lightest subgraphs, providing a slightly slower combinatorial algorithm.

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“…Hoàng et al [12] showed that Algorithm 1 runs in O(m+(#P 3 )+(#K 3 )) time, where (#P 3 ) and (#K 3 ) are the number of P 3 's and K 3 's, respectively: The algorithm considers each edge uv and each vertex w incident with uv. Thus, u, v, and w form either a P 3 or a triangle.…”

Section: Observation 3 (Folklore)mentioning

confidence: 99%

Detecting and Enumerating Small Induced Subgraphs in $c$-Closed Graphs

Koana¹,

Nichterlein²

2020

Preprint

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Fox et al. [SIAM J. Comp. 2020] introduced a new parameter, called c-closure, for a parameterized study of clique enumeration problems. A graph G is c-closed if every pair of vertices with at least c common neighbors is adjacent. The c-closure of G is the smallest c such that G is c-closed. We systematically explore the impact of c-closure on the computational complexity of detecting and enumerating small induced subgraphs. More precisely, for each graph H on three or four vertices, we investigate parameterized polynomial-time algorithms for detecting H and for enumerating all occurrences of H in a given c-closed graph.

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Finding and listing induced paths and cycles

Cited by 12 publications

References 10 publications

Best match graphs and reconciliation of gene trees with species trees

Best match graphs and reconciliation of gene trees with species trees

Detecting and Counting Small Pattern Graphs

Detecting and Enumerating Small Induced Subgraphs in $c$-Closed Graphs

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