✦ LIBER ✦

Some theorems on graphs and posets

✍ Scribed by William T. Trotter Jr.; John I. Moore Jr.

Publisher: Elsevier Science
Year: 1976
Tongue: English
Weight: 800 KB
Volume: 15
Category: Article
ISSN: 0012-365X
DOI: 10.1016/0012-365x(76)90111-4

No coin nor oath required. For personal study only.

✦ Synopsis

In this journal, Lcclerc proved that the dimension of the partiailly ordered slet consisting of all subf~ce'~ of a tree T, m&red by inclusion, is the number of end yuints of 'I'. Leclerc posed the probkrn of determitAng the dimension the partially ed set P consisting of all inducxxI connected subgraphs of a connec graph G for tPisa lattice.

In this paper, WC prove that the poset P consisting af all induced connected subgraphs of a nontrivial connected graph G, partially ordered by inclusion, has dimcnsior. n whcrc n is the number of rtioncut vertices in G wheehcr or not P is a fatticc. We also dctcrmine the ditnensian of the distrilbutivc Iattic?-of all subgraphs of a 6 {ph.

The dimension of' a partialfy ordered set (X, P) was defi lm!l ] as H-w minimum nuflhcr of linear orders on intersection is l? A goset has ciiinensicm one if and only if it is a chain. In [ 61 Leclorc proved the fol2owing result which gives an alternate rmitim of dismzsion for hs~,: posets which are not chains.

📜 SIMILAR VOLUMES

On some factor theorems of graphs

✍ Mao-cheng Cai 📂 Article 📅 1991 🏛 Elsevier Science 🌐 English ⚖ 362 KB

The aim of this note is to show that some recently published results on graph factors derive fairly easily from Lovrisz' (g,f)-factor theorems.

Posets and planar graphs

✍ Stefan Felsner; William T. Trotter 📂 Article 📅 2005 🏛 John Wiley and Sons 🌐 English ⚖ 112 KB

## Abstract Usually __dimension__ should be an integer valued parameter. We introduce a refined version of dimension for graphs, which can assume a value [__t__ − 1 ↕ __t__], thought to be between __t__ − 1 and __t__. We have the following two results: (a) a graph is outerplanar if and only if its

Graph coloring and monotone functions on

Graph coloring and monotone functions on posets

✍ Nathan Linial 📂 Article 📅 1986 🏛 Elsevier Science 🌐 English ⚖ 79 KB

The purpose of this note is to point out a relationship between graph coloring and monotone functions defined on posets. This relationship permits us to deduce certain properties of the chromatic polynomial of a graph.

Median graphs, parallelism and posets

✍ Jean-Pierre Barthélemy; Julien Constantin 📂 Article 📅 1993 🏛 Elsevier Science 🌐 English ⚖ 989 KB

A notion of parallelism is defined in finite median graphs and a number of properties about geodesics and the existence of cubes are obtained. Introducing sites as a double structure of partial order and graph on a set, it is shown that all median graphs can be constructed from sites and, in fact, t

Some theorems of uniquely pancyclic grap

Some theorems of uniquely pancyclic graphs

✍ Yongbing Shi 📂 Article 📅 1986 🏛 Elsevier Science 🌐 English ⚖ 773 KB

Disjoint circuits on a Klein bottle and

Disjoint circuits on a Klein bottle and a theorem on posets

✍ Guoli Ding 📂 Article 📅 1993 🏛 Elsevier Science 🌐 English ⚖ 694 KB

Ding, G., Disjoint circuits on a Klein bottle and a theorem on posets, Discrete Mathematics 112 (1993) 81-91. In this paper, we consider the problem of packing disjoint directed circuits in a digraph drawn on the Klein bottle or on the torus. We formulate a problem on posets which unifies all the p