Lettericity of graphs: an FPT algorithm and a bound on the size of obstructions
Lettericity is a graph parameter responsible for many attractive structural properties. In particular, graphs of bounded lettericity have bounded linear clique-width and they are well-quasi-ordered by induced subgraphs. The latter property implies that any hereditary class of graphs of bounded lette...
Uložené v:
| Vydané v: | Algorithmica |
|---|---|
| Hlavní autori: | , , , |
| Médium: | Journal Article |
| Jazyk: | English |
| Vydavateľské údaje: |
Springer Verlag
19.02.2024
|
| Predmet: | |
| ISSN: | 0178-4617, 1432-0541 |
| On-line prístup: | Získať plný text |
| Tagy: |
Pridať tag
Žiadne tagy, Buďte prvý, kto otaguje tento záznam!
|
| Abstract | Lettericity is a graph parameter responsible for many attractive structural properties. In particular, graphs of bounded lettericity have bounded linear clique-width and they are well-quasi-ordered by induced subgraphs. The latter property implies that any hereditary class of graphs of bounded lettericity can be described by finitely many forbidden induced subgraphs. This, in turn, implies, in a non-constructive way, polynomial-time recognition of such classes. However, no constructive algorithms and no specific bounds on the size of forbidden graphs are available up to date. In the present paper, we develop an algorithm that recognizes $n$-vertex graphs of lettericity at most $k$ in time $f(k)n^3$ and show that any minimal graph of lettericity more than $k$ has at most $2^{O(k^2\log k)}$ vertices. |
|---|---|
| AbstractList | Lettericity is a graph parameter responsible for many attractive structural properties. In particular, graphs of bounded lettericity have bounded linear clique-width and they are well-quasi-ordered by induced subgraphs. The latter property implies that any hereditary class of graphs of bounded lettericity can be described by finitely many forbidden induced subgraphs. This, in turn, implies, in a non-constructive way, polynomial-time recognition of such classes. However, no constructive algorithms and no specific bounds on the size of forbidden graphs are available up to date. In the present paper, we develop an algorithm that recognizes $n$-vertex graphs of lettericity at most $k$ in time $f(k)n^3$ and show that any minimal graph of lettericity more than $k$ has at most $2^{O(k^2\log k)}$ vertices. |
| Author | Alecu, Bogdan Zamaraev, Viktor Kanté, Mamadou Moustapha Lozin, Vadim |
| Author_xml | – sequence: 1 givenname: Bogdan surname: Alecu fullname: Alecu, Bogdan organization: Warwick Mathematics Institute – sequence: 2 givenname: Mamadou Moustapha orcidid: 0000-0003-1838-7744 surname: Kanté fullname: Kanté, Mamadou Moustapha organization: Laboratoire d'Informatique, de Modélisation et d'Optimisation des Systèmes – sequence: 3 givenname: Vadim surname: Lozin fullname: Lozin, Vadim organization: Warwick Mathematics Institute – sequence: 4 givenname: Viktor surname: Zamaraev fullname: Zamaraev, Viktor organization: University of Liverpool |
| BackLink | https://hal.science/hal-04859243$$DView record in HAL |
| BookMark | eNotkE9rwjAYh8NwMHX7ALvlukPdm39Nu5vI1EHBHTzsVt6mqc3QRpIouE8_ZTs98MDvOfwmZDT4wRLyzGAmC6XgFcOXO8-4BD5jXKnyjoyZFDwDJdmIjIHpIpM50w9kEuM3AOO6zMdkU9mUbHDGpQv1Hd0FPPbxjeJAl59bivudDy71h6toKdLGn670A029pdH92NvGNzGFk0nOD_GR3He4j_bpn1OyXb5vF-us2qw-FvMqQ1WwrBCtAsO5wrIzEkB3bSOEMZ3QRnAFAhuNquVFXkphpTKSdVwx0eYaQGIhpuTlL9vjvj4Gd8BwqT26ej2v6puD6ysll-LMxC9JVFOe |
| ContentType | Journal Article |
| Copyright | Distributed under a Creative Commons Attribution 4.0 International License |
| Copyright_xml | – notice: Distributed under a Creative Commons Attribution 4.0 International License |
| DBID | 1XC |
| DOI | 10.48550/arXiv.2402.12559 |
| DatabaseName | Hyper Article en Ligne (HAL) |
| DatabaseTitleList | |
| DeliveryMethod | fulltext_linktorsrc |
| Discipline | Computer Science |
| EISSN | 1432-0541 |
| ExternalDocumentID | oai:HAL:hal-04859243v1 |
| GroupedDBID | -Y2 -~C -~X .86 .DC .VR 06D 0R~ 0VY 199 1N0 1SB 1XC 203 23M 28- 2J2 2JN 2JY 2KG 2KM 2LR 2P1 2VQ 2~H 30V 4.4 406 408 409 40D 40E 5GY 5QI 5VS 67Z 6NX 78A 8TC 8UJ 95- 95. 95~ 96X AAAVM AABHQ AACDK AAHNG AAIAL AAJBT AAJKR AANZL AAOBN AAPKM AARHV AARTL AASML AATNV AATVU AAUYE AAWCG AAYIU AAYQN AAYTO ABAKF ABBBX ABBRH ABBXA ABDBE ABDPE ABDZT ABECU ABFSG ABFSI ABFTV ABHLI ABHQN ABJNI ABJOX ABKCH ABKTR ABLJU ABMNI ABMQK ABNWP ABQBU ABQSL ABRTQ ABSXP ABTEG ABTHY ABTKH ABTMW ABULA ABWNU ABXPI ACAOD ACBXY ACDTI ACGFS ACHSB ACHXU ACKNC ACMDZ ACMLO ACOKC ACOMO ACPIV ACSTC ACZOJ ADHHG ADHIR ADHKG ADIMF ADKNI ADKPE ADRFC ADTPH ADURQ ADYFF ADZKW AEBTG AEFIE AEFQL AEGAL AEGNC AEJHL AEJRE AEKMD AEMSY AENEX AEOHA AEPYU AESKC AETLH AEVLU AEXYK AEZWR AFBBN AFDZB AFEXP AFGCZ AFHIU AFLOW AFOHR AFQWF AFWTZ AFZKB AGAYW AGDGC AGGDS AGJBK AGMZJ AGQEE AGQMX AGQPQ AGRTI AGWIL AGWZB AGYKE AHAVH AHBYD AHKAY AHPBZ AHSBF AHWEU AHYZX AI. AIAKS AIGIU AIIXL AILAN AITGF AIXLP AJBLW AJRNO AJZVZ ALMA_UNASSIGNED_HOLDINGS ALWAN AMKLP AMXSW AMYLF AMYQR AOCGG ARMRJ ASPBG ATHPR AVWKF AXYYD AYFIA AYJHY AZFZN B-. BA0 BBWZM BDATZ BGNMA BSONS CAG COF CS3 CSCUP DDRTE DL5 DNIVK DPUIP E.L EBLON EBS EIOEI EJD ESBYG FEDTE FERAY FFXSO FIGPU FINBP FNLPD FRRFC FSGXE FWDCC GGCAI GGRSB GJIRD GNWQR GQ7 GQ8 GXS H13 HF~ HG5 HG6 HMJXF HQYDN HRMNR HVGLF HZ~ H~9 I09 IHE IJ- IKXTQ ITM IWAJR IXC IZIGR IZQ I~X I~Z J-C J0Z JBSCW JCJTX JZLTJ KDC KOV KOW LAS LLZTM M4Y MA- N2Q N9A NB0 NDZJH NPVJJ NQJWS NU0 O9- O93 O9G O9I O9J OAM P19 P9O PF- PT4 PT5 QOK QOS R4E R89 R9I RHV RNI RNS ROL RPX RSV RZK S16 S1Z S26 S27 S28 S3B SAP SCJ SCLPG SCO SDH SDM SHX SISQX SJYHP SNE SNPRN SNX SOHCF SOJ SPISZ SRMVM SSLCW STPWE SZN T13 T16 TN5 TSG TSK TSV TUC U2A UG4 UOJIU UQL UTJUX UZXMN VC2 VFIZW VH1 W23 W48 WK8 YLTOR Z45 ZMTXR ZY4 ~EX |
| ID | FETCH-LOGICAL-a581-83d50c225a9fc4007fdb33ccf37c32503ab7a5d286943e45c41f2513d67004a83 |
| ISSN | 0178-4617 |
| IngestDate | Tue Oct 28 06:37:10 EDT 2025 |
| IsDoiOpenAccess | false |
| IsOpenAccess | true |
| IsPeerReviewed | true |
| IsScholarly | true |
| Keywords | Discrete Mathematics (cs.DM) FOS: Computer and information sciences FOS: Mathematics Data Structures and Algorithms (cs.DS) Combinatorics (math.CO) |
| Language | English |
| License | Distributed under a Creative Commons Attribution 4.0 International License: http://creativecommons.org/licenses/by/4.0 |
| LinkModel | OpenURL |
| MergedId | FETCHMERGED-LOGICAL-a581-83d50c225a9fc4007fdb33ccf37c32503ab7a5d286943e45c41f2513d67004a83 |
| ORCID | 0000-0003-1838-7744 |
| OpenAccessLink | https://arxiv.org/abs/2402.12559 |
| ParticipantIDs | hal_primary_oai_HAL_hal_04859243v1 |
| PublicationCentury | 2000 |
| PublicationDate | 2024-02-19 |
| PublicationDateYYYYMMDD | 2024-02-19 |
| PublicationDate_xml | – month: 02 year: 2024 text: 2024-02-19 day: 19 |
| PublicationDecade | 2020 |
| PublicationTitle | Algorithmica |
| PublicationYear | 2024 |
| Publisher | Springer Verlag |
| Publisher_xml | – name: Springer Verlag |
| SSID | ssj0012796 |
| Score | 2.3673778 |
| SecondaryResourceType | preprint |
| Snippet | Lettericity is a graph parameter responsible for many attractive structural properties. In particular, graphs of bounded lettericity have bounded linear... |
| SourceID | hal |
| SourceType | Open Access Repository |
| SubjectTerms | Computational Complexity Computer Science Data Structures and Algorithms Discrete Mathematics |
| Title | Lettericity of graphs: an FPT algorithm and a bound on the size of obstructions |
| URI | https://hal.science/hal-04859243 |
| hasFullText | 1 |
| inHoldings | 1 |
| isFullTextHit | |
| isPrint | |
| journalDatabaseRights | – providerCode: PRVAVX databaseName: SpringerLINK Contemporary 1997-Present customDbUrl: eissn: 1432-0541 dateEnd: 99991231 omitProxy: false ssIdentifier: ssj0012796 issn: 0178-4617 databaseCode: RSV dateStart: 19970101 isFulltext: true titleUrlDefault: https://link.springer.com/search?facet-content-type=%22Journal%22 providerName: Springer Nature |
| link | http://cvtisr.summon.serialssolutions.com/2.0.0/link/0/eLvHCXMwtV3Nb9MwFLeqwYELMD7E52QhbpVLEzuzwy2CVUWrSsWqqbfIH8karUuqdlTT7vzfPNtJmiEO48DFqpy4cvx-eXnfD6GP2VDoPKCcBMrkhCluiIDXiISx4VFuszGlq64_4dOpWCziWa_3q8mF2a14WYqbm3j9X0kNc0Bsmzr7D-Ru_xQm4DcQHUYgO4z3IrxP0Cl0HWvhKlK7uDd4k0ezeV-uLqpNcb30vTFkX9nGSrXPoL8tbp0RoVJtYdltV35NmsWdEJ_ENth1OKkuzB5sp0Az74b3OUFX0lQ_gYfYjK31sl09qW59GYNzaYqr1o4Nt28kPLq9UFz6ksiteSJkNqK5wwQb82S_Y56sLZmgvrJjn7g5yDz3ZTQkIEMGf-PtrvSa_XJtFsVuYJ1Cg8DqQ_sPWeO8Hydn6ezrKJ18m57evdoJPhwnExiXckWAh0WghdIdKNEPQh7Fljn-ODtvnVEhd23e2h1757jbz6c_dwMiyrIxyTsRZf4UPa51C5x4TByiXlY-Q0-avh24ZuPP0fcORHCVYw-Rz1iWGACCW4DAhMESO4DgqsQAEGwBYtd0AfICzUcn8y9jUjfWIDISARHUREMNjFzGuQYeznOjKNU6p1xTEImpVFxGJhTHMaMZizQLchCDqbEpXUwK-hIdlFWZvUI4G-aB5krqSAdW1hPMKC2UcZIoqO6v0Qc4jnTtK6ektpY5HHxq5_bH_uY-N71Fj_bweocO4Bmz9-ih3l0X282RI9hv8whigg |
| linkProvider | Springer Nature |
| openUrl | ctx_ver=Z39.88-2004&ctx_enc=info%3Aofi%2Fenc%3AUTF-8&rfr_id=info%3Asid%2Fsummon.serialssolutions.com&rft_val_fmt=info%3Aofi%2Ffmt%3Akev%3Amtx%3Ajournal&rft.genre=article&rft.atitle=Lettericity+of+graphs%3A+an+FPT+algorithm+and+a+bound+on+the+size+of+obstructions&rft.jtitle=Algorithmica&rft.au=Alecu%2C+Bogdan&rft.au=Kant%C3%A9%2C+Mamadou+Moustapha&rft.au=Lozin%2C+Vadim&rft.au=Zamaraev%2C+Viktor&rft.date=2024-02-19&rft.pub=Springer+Verlag&rft.issn=0178-4617&rft.eissn=1432-0541&rft_id=info:doi/10.48550%2FarXiv.2402.12559&rft.externalDBID=HAS_PDF_LINK&rft.externalDocID=oai%3AHAL%3Ahal-04859243v1 |
| thumbnail_l | http://covers-cdn.summon.serialssolutions.com/index.aspx?isbn=/lc.gif&issn=0178-4617&client=summon |
| thumbnail_m | http://covers-cdn.summon.serialssolutions.com/index.aspx?isbn=/mc.gif&issn=0178-4617&client=summon |
| thumbnail_s | http://covers-cdn.summon.serialssolutions.com/index.aspx?isbn=/sc.gif&issn=0178-4617&client=summon |