A linear colouring of a graph is a proper vertex colouring such that the subgraph induced by any two colour classes is a set of vertex disjoint paths. The corresponding linear chromatic number of a graph G, namely lc(G), is the minimum number of colours in a linear colouring of G. We prove that for a graph G with girth g ≥ 8 and maximum degree ∆ ≥ 7 the inequality on its linear colouring number...

An equitable colouring of a balanced G-design (X,B) is a map φ∶B → C such that ∣bi(x) − bj(x)∣ ≤ 1 for any x ∈ X and i, j, with i ≠ j, being bi(x) the number of blocks containing the vertex x and coloured with the colour i. A c-colouring is a colouring in which exactly c colours are used. A c-colouring of type s is a colourings in which, for every vertex x, all the blocks containing x are colou...

In this paper, a colouring game and two versions of marking games (the weak and the strong) on digraphs are studied. We introduce the weak game chromatic number χwg(D) and the weak game colouring number wgcol(D) of digraphs D. It is proved that if D is an oriented planar graph, then χwg(D) 6 wgcol(D) 6 9, and if D is an oriented outerplanar graph, then χwg(D) 6 wgcol(D) 6 4. Then we study the s...

A vertex colouring assigns to each vertex of a graph a colour such that adjacent vertices have different colours. The algorithmic complexity of the Colouring problem, asking for the smallest number of colours needed to vertex-colour a given graph, is known for a large number of graph classes. Notably it is NP-complete in general, but polynomial time solvable for perfect graphs. A triple of vert...

The distribution of carbon (C) into whole grapevine fruiting cuttings was investigated during flower development to determine the relative contribution of inflorescence and leaf photoassimilates in the total C balance and to investigate their partitioning towards other plant organs. A (13)C labelling procedure was used to label C photoassimilates by leaves and inflorescences in grapevine. Inves...

Flowering of Arabidopsis thaliana is induced by exposure to long days (LDs). During this process, the shoot apical meristem is converted to an inflorescence meristem that forms flowers, and this transition is maintained even if plants are returned to short days (SDs). We show that exposure to five LDs is sufficient to commit the meristem of SD-grown plants to flower as if they were exposed to c...

Let G be a simple graph and (G) denote the maximum degree of G. A harmonious colouring of G is a proper vertex colouring such that each pair of colours appears together on at most one edge. The harmonious chromatic number h(G) is the least number of colours in such a colouring. In this paper it is shown that if T is a tree of order n and (T ) n2 , then there exists a harmonious colouring of T w...

The anatomy of leaves and inflorescence axes of Spathanthus (2 spp.), Rapatea (2 spp.), Cephalostemon (1 sp.), and Duckea (1 sp.) (Rapateoideae, Rapateaceae) was studied to identify useful characters for taxonomy. The cross-section shape of inflorescence axis differentiates the genera, while the cross-section shape and structure of leaf midrib has a specific value. The following characteristics...

to study the effect of plant density and planting pattern on iranian ox-tongue, an experiment carried out with two factors: planting pattern (square and rectangular pattern) and plant density (2, 4, 6, 8 plant m-2) in a factorial test performed based on rcbd in 3 replications during 2009-2010 in latmahalleh eshkevarat village in guilan province, iran. characteristics that measured included: dry...