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Minimal κ-connected Graphs with Small Number of Vertices of Degree κ

Karpov D. V.

Fundamenta Informaticae

2016

Vol. 145, nr 3

279--312

On Normal Forms and Erasing Rules in Path Controlled Grammars

Koutnŷ J., Meduna A.

Schedae Informaticae

2013

Vol. 22

9--18

This paper discusses path controlled grammars { context-free gram- mars with a root-to-leaf path in their derivation trees restricted by a control language. First, it investigates the impact of erasing rules on the generative power of path controlled grammars. Then, it establishes two Chomsky-like normal forms for path controlled grammars - the first allows unit rules, the second allows just one erasing rule.

[r, s, t]-colourings of paths

Salvador Villa M., Schiermeyer I.

Opuscula Mathematica

2007

Vol. 27, no. 1

131-149

The concept of [r, s, t]-colourings was recently introduced by Hackmann, Kemnitz and Marangio [3] as follows: Given non-negative integers r, s and t, an [r, s, t]-colouring of a graph G = (V(G), E(G)) is a mapping c from V(G) ∪ E(G) to the colour set {1, 2,..., k} such that ‌c(vi) - c(vj)‌ ≥ r for every two adjacent vertices vi, vj, ‌c(ei) - c(ej)‌ ≥ s for every two adjacent edges ei, ej, and ‌c(vi) - c(ej)‌ ≥ t for all pairs of incident vertices and edges, respectively. The [r, s, t]-chromatic number Xr,s,t(G) of G is defined to be the minimum k such that G admits an [r, s, t]-colouring. In this paper, we determine the [r, s, t]-chromatic number for paths.