𝔖 Bobbio Scriptorium
✦   LIBER   ✦

Survey of results on the maximum genus of a graph

✍ Scribed by Richard D. Ringeisen


Publisher
John Wiley and Sons
Year
1979
Tongue
English
Weight
619 KB
Volume
3
Category
Article
ISSN
0364-9024

No coin nor oath required. For personal study only.

✦ Synopsis


Abstract

Some of the early questions concerning the maximum genus of a graph have now been answered. In this paper we survey the progress made on such problems and present some recent results, outlining proofs for some of the major theorems.


πŸ“œ SIMILAR VOLUMES


A tight lower bound on the maximum genus
✍ Jianer Chen; Saroja P. Kanchi; Jonathan L. Gross πŸ“‚ Article πŸ“… 1996 πŸ› Elsevier Science 🌐 English βš– 856 KB

It is proved that every connected simplicial graph with minimum valence at least three has maximum genus at least one-quarter of its cycle rank. This follows from the technical result that every 3-regular simplicial graph except K4 has a Xuong co-tree whose odd components have only one edge each. It

The maximum genus of vertex-transitive g
✍ Martin Ε koviera; Roman Nedela πŸ“‚ Article πŸ“… 1989 πŸ› Elsevier Science 🌐 English βš– 911 KB

The maximum genus of all vertex-transitive graphs is computed. It is proved that a k-valent vertex-transitive graph of girth g is upper-embeddable whenever k 3 4 or g 2 4. Non-upper-embeddable vertex-transitive graphs are characterized. A particular attention is paid to Cayley graphs. Groups for wh

The maximum genus of graphs of diameter
✍ Martin Ε koviera πŸ“‚ Article πŸ“… 1991 πŸ› Elsevier Science 🌐 English βš– 400 KB

Skoviera, M., The maximum genus of graphs of diameter two, Discrete Mathematics 87 (1991) 175-180. Let G be a (finite) graph of diameter two. We prove that if G is loopless then it is upper embeddable, i.e. the maximum genus y,&G) equals [fi(G)/Z], where /3(G) = IF(G)1 -IV(G)1 + 1 is the Betti numbe

Face Size and the Maximum Genus of a Gra
✍ Yuanqiu Huang; Yanpei Liu πŸ“‚ Article πŸ“… 2000 πŸ› Elsevier Science 🌐 English βš– 150 KB

This paper shows that a simple graph which can be cellularly embedded on some closed surface in such a way that the size of each face does not exceed 7 is upper embeddable. This settles one of two conjectures posed by Nedela and S8 koviera (1990, in ``Topics in Combinatorics and Graph Theory,'' pp.

The maximum interval number of graphs wi
✍ Edward R. Scheinerman πŸ“‚ Article πŸ“… 1987 πŸ› John Wiley and Sons 🌐 English βš– 202 KB πŸ‘ 1 views

The interval number of a graph G, denoted i(G), is the least positive integer t such that G is the intersection graph of sets, each of which is the union of t compact real intervals. It is known that every planar graph has interval number at most 3 and that this result is best possible. We investiga