A fast deterministic detection of small pattern graphs in graphs without large cliques
(2017) 11th International Conference and Workshops on Algorithms and Computation, WALCOM 2017 In WALCOM: Algorithms and Computation  11th International Conference and Workshops, WALCOM 2017, Proceedings 10167 LNCS. p.217227 Abstract
We show that for several pattern graphs on four vertices (e.g., C_{4}), their induced copies in host graphs with n vertices and no clique on k + 1 vertices can be deterministically detected in time Õ (n^{ω}k^{μ} + n^{2}k^{2}), where Õ (f) stands for O(f(log f)^{c}) for some constant c, and μ ≈ 0. 46530. The aforementioned pattern graphs have a pair of nonadjacent vertices whose neighborhoods are equal. By considering dual graphs, in the same asymptotic time, we can also detect four vertex pattern graphs, that have an adjacent pair of vertices with the same neighbors among the remaining vertices (e.g., K_{4}), in host graphs with n vertices and no independent set on k + 1 vertices.... (More)
We show that for several pattern graphs on four vertices (e.g., C_{4}), their induced copies in host graphs with n vertices and no clique on k + 1 vertices can be deterministically detected in time Õ (n^{ω}k^{μ} + n^{2}k^{2}), where Õ (f) stands for O(f(log f)^{c}) for some constant c, and μ ≈ 0. 46530. The aforementioned pattern graphs have a pair of nonadjacent vertices whose neighborhoods are equal. By considering dual graphs, in the same asymptotic time, we can also detect four vertex pattern graphs, that have an adjacent pair of vertices with the same neighbors among the remaining vertices (e.g., K_{4}), in host graphs with n vertices and no independent set on k + 1 vertices. By using the concept of Ramsey numbers, we can extend our method for induced subgraph isomorphism to include larger pattern graphs having a set of independent vertices with the same neighborhood and nvertex host graphs without cliques on k+1 vertices (as well as the pattern graphs and host graphs dual to the aforementioned ones, respectively).
(Less)
 author
 Kowaluk, Mirosław and Lingas, Andrzej ^{LU}
 organization
 publishing date
 2017
 type
 Chapter in Book/Report/Conference proceeding
 publication status
 published
 subject
 keywords
 Induced subgraph isomorphism, Matrix multiplication, Time complexity, Witnesses for boolean matrix product
 in
 WALCOM: Algorithms and Computation  11th International Conference and Workshops, WALCOM 2017, Proceedings
 volume
 10167 LNCS
 pages
 11 pages
 publisher
 Springer Verlag
 conference name
 11th International Conference and Workshops on Algorithms and Computation, WALCOM 2017
 external identifiers

 scopus:85014185907
 wos:000413067200017
 ISSN
 03029743
 16113349
 ISBN
 9783319539249
 DOI
 10.1007/9783319539256_17
 language
 English
 LU publication?
 yes
 id
 2b240aef7f3741e9ad24085acf5064b5
 date added to LUP
 20170315 12:38:55
 date last changed
 20180116 13:24:52
@inproceedings{2b240aef7f3741e9ad24085acf5064b5, abstract = {<p>We show that for several pattern graphs on four vertices (e.g., C<sub>4</sub>), their induced copies in host graphs with n vertices and no clique on k + 1 vertices can be deterministically detected in time Õ (n<sup>ω</sup>k<sup>μ</sup> + n<sup>2</sup>k<sup>2</sup>), where Õ (f) stands for O(f(log f)<sup>c</sup>) for some constant c, and μ ≈ 0. 46530. The aforementioned pattern graphs have a pair of nonadjacent vertices whose neighborhoods are equal. By considering dual graphs, in the same asymptotic time, we can also detect four vertex pattern graphs, that have an adjacent pair of vertices with the same neighbors among the remaining vertices (e.g., K<sub>4</sub>), in host graphs with n vertices and no independent set on k + 1 vertices. By using the concept of Ramsey numbers, we can extend our method for induced subgraph isomorphism to include larger pattern graphs having a set of independent vertices with the same neighborhood and nvertex host graphs without cliques on k+1 vertices (as well as the pattern graphs and host graphs dual to the aforementioned ones, respectively).</p>}, author = {Kowaluk, Mirosław and Lingas, Andrzej}, booktitle = {WALCOM: Algorithms and Computation  11th International Conference and Workshops, WALCOM 2017, Proceedings}, isbn = {9783319539249}, issn = {03029743}, keyword = {Induced subgraph isomorphism,Matrix multiplication,Time complexity,Witnesses for boolean matrix product}, language = {eng}, pages = {217227}, publisher = {Springer Verlag}, title = {A fast deterministic detection of small pattern graphs in graphs without large cliques}, url = {http://dx.doi.org/10.1007/9783319539256_17}, volume = {10167 LNCS}, year = {2017}, }