𝔖 Bobbio Scriptorium
✦   LIBER   ✦

Classes of interval graphs under expanding length restrictions

✍ Scribed by P. C. Fishburn; R. L. Graham

Publisher
John Wiley and Sons
Year
1985
Tongue
English
Weight
630 KB
Volume
9
Category
Article
ISSN
0364-9024

No coin nor oath required. For personal study only.

✦ Synopsis

Let C(a) denote the finite interval graphs representable as intersection graphs of closed real intervals with lengths in (1, a]. The points of increase for C are the rational a > 1. The set D(a) = [n,,,C(p)l\C(a) of graphs that appear as soon as we go past a is characterized up to isomorphism on the basis of finite sets €(a) of irreducible graphs for each rational a. With a = p/q and p and 9 relatively prime, \€(a)\ is computed for all (p, q) with 9 s 2 and p = q + 1. When 9 = 1, €(p) contains only the bipartite star K,,p+2. A lower bound on (€(a)( is given for all rational a.

πŸ“œ SIMILAR VOLUMES

Class of graphs with restricted neighbor
Class of graphs with restricted neighborhoods
✍ Kim T. Rawlinson; R. C. Entringer πŸ“‚ Article πŸ“… 1979 πŸ› John Wiley and Sons 🌐 English βš– 286 KB

## Abstract A description is obtained for connected graphs in which a point __u__ is adjacent of __v__ only if __u__ is adjacent to all points whose degree is greater than that of __v__. The minimum number of lines in such a grpah with all points having degree at least __d__ is also determined. Fin

Orderly algorithms for generating restri
Orderly algorithms for generating restricted classes of graphs
✍ Charles J. Colbourn; Ronald C. Read πŸ“‚ Article πŸ“… 1979 πŸ› John Wiley and Sons 🌐 English βš– 463 KB

## Abstract Orderly algorithms for the generation of exhaustive lists of nonisomorphic graphs are discussed. The existence of orderly methods to generate the graphs with a given subgraph and without a given subgraph is established. This method can be used to list all the nonisomorphic subgraphs of

The total interval number of a graph, I:
The total interval number of a graph, I: Fundamental classes
✍ Thomas M. Kratzke; Douglas B. West πŸ“‚ Article πŸ“… 1993 πŸ› Elsevier Science 🌐 English βš– 906 KB

Kratzke, T.M. and D.B. West, The total interval number of a graph, I: Fundamental classes, Discrete Mathematics 118 (1993) 145-156. A multiple-interval representation of a simple graph G assigns each vertex a union of disjoint real intervals, such that vertices are adjacent if and only if their assi

Swing-up and stabilization of a cart–pen
Swing-up and stabilization of a cart–pendulum system under restricted cart track length
✍ Debasish Chatterjee; Amit Patra; Harish K. Joglekar πŸ“‚ Article πŸ“… 2002 πŸ› Elsevier Science 🌐 English βš– 218 KB

This paper describes the swing-up and stabilization of a cart-pendulum system with a restricted cart track length and restricted control force using generalized energy control methods. Starting from a pendant position, the pendulum is swung up to the upright unstable equilibrium conΓΏguration using e

Peptide length-dependent TCR antagonism
Peptide length-dependent TCR antagonism on class II HLA-restricted responses of peripheral blood mononuclear cells and T cell clones
✍ Sho Matsushita; Takako Matsuoka πŸ“‚ Article πŸ“… 1999 πŸ› John Wiley and Sons 🌐 English βš– 147 KB

T cell clonal recognition of peptide ligands is highly diverse. To investigate how peptide mixtures with diverse sequences affect polyclonal responses of peripheral blood mononuclear cells (PBMC), we synthesized Xn (n = 9-19) peptides that consist of 9 to 19 residues with random sequences. We found