Density of universal classes of series-parallel graphs - Archive ouverte HAL Accéder directement au contenu
Communication Dans Un Congrès Discrete Mathematics and Theoretical Computer Science Année : 2005

Density of universal classes of series-parallel graphs

Résumé

A class of graphs $\mathcal{C}$ ordered by the homomorphism relation is universal if every countable partial order can be embedded in $\mathcal{C}$. It was shown in [ZH] that the class $\mathcal{C_k}$ of $k$-colorable graphs, for any fixed $k≥3$, induces a universal partial order. In [HN1], a surprisingly small subclass of $\mathcal{C_3}$ which is a proper subclass of $K_4$-minor-free graphs $(\mathcal{G/K_4)}$ is shown to be universal. In another direction, a density result was given in [PZ], that for each rational number $a/b ∈[2,8/3]∪ \{3\}$, there is a $K_4$-minor-free graph with circular chromatic number equal to $a/b$. In this note we show for each rational number $a/b$ within this interval the class $\mathcal{K_{a/b}}$ of $0K_4$-minor-free graphs with circular chromatic number $a/b$ is universal if and only if $a/b ≠2$, $5/2$ or $3$. This shows yet another surprising richness of the $K_4$-minor-free class that it contains universal classes as dense as the rational numbers.
Fichier principal
Vignette du fichier
dmAE0149.pdf (166.75 Ko) Télécharger le fichier
Origine Fichiers éditeurs autorisés sur une archive ouverte
Loading...

Dates et versions

hal-01184364 , version 1 (14-08-2015)

Identifiants

Citer

Jaroslav Nešetřil, Yared Nigussie. Density of universal classes of series-parallel graphs. 2005 European Conference on Combinatorics, Graph Theory and Applications (EuroComb '05), 2005, Berlin, Germany. pp.245-250, ⟨10.46298/dmtcs.3407⟩. ⟨hal-01184364⟩

Collections

TDS-MACS
116 Consultations
662 Téléchargements

Altmetric

Partager

Gmail Mastodon Facebook X LinkedIn More