A Proof of the Alternate Thomassé Conjecture for Countable N-Free Posets

被引：0

作者：

Abdi, Davoud ^{[1
]}

机构：

[1] Univ Calgary, Dept Math & Stat, Calgary, AB T2N 1N4, Canada

来源：

ORDER-A JOURNAL ON THE THEORY OF ORDERED SETS AND ITS APPLICATIONS | 2024年 / 41卷 / 03期

关键词：

Siblings; Posets; Decomposition trees; GRAPHS;

D O I：

10.1007/s11083-023-09650-w

中图分类号：

O1 [数学];

学科分类号：

0701 ; 070101 ;

摘要：

An N-free poset is a poset whose comparability graph does not embed an induced path with four vertices. We use the well-quasi-order property of the class of countable N-free posets and some labelled ordered trees to show that a countable N-free poset has one or infinitely many siblings, up to isomorphism. This, partially proves a conjecture stated by Thomasse for this class.

引用

页码：613 / 641

页数：29

共 21 条

[1]

Abdi D., 2022, ARXIV

[2]

Abdi D., 2022, SIBLINGS DIRECT SUMS

[3] Twins of rayless graphs [J].

Bonato, Anthony ;

Bruhn, Henning ;

Diestel, Reinhard ;

Spruessel, Philipp .

JOURNAL OF COMBINATORIAL THEORY SERIES B, 2011, 101 (01) :60-65

[4] Mutually embeddable graphs and the tree alternative conjecture [J].

Bonato, Anthony ;

Tardif, Claude .

JOURNAL OF COMBINATORIAL THEORY SERIES B, 2006, 96 (06) :874-880

[5] Prechains and self duality [J].

Boudabbous, Youssef ;

Delhomme, Christian .

DISCRETE MATHEMATICS, 2012, 312 (10) :1743-1765

[6]

Braunfeld S., 2021, ARXIV

[7] The modular decomposition of countable graphs. Definition and construction in monadic second-order logic [J].

Courcelle, Bruno ;

Delhomme, Christian .

THEORETICAL COMPUTER SCIENCE, 2008, 394 (1-2) :1-38

[8] N-FREE POSETS AS GENERALIZATIONS OF SERIES-PARALLEL POSETS [J].

HABIB, M ;

JEGOU, R .

DISCRETE APPLIED MATHEMATICS, 1985, 12 (03) :279-291

[9]

Hahn G., 2020, ARXIV

[10] CLASS OF POSETS AND CORRESPONDING COMPARABILITY GRAPHS [J].

JUNG, HA .

JOURNAL OF COMBINATORIAL THEORY SERIES B, 1978, 24 (02) :125-133

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