We study the following one-person game against a random graph: the Player’s goal is to 2-colour a random sequence of edges e1, e2, . . . of a complete graph on n vertices, avoiding a monochromatic triangle for as long as possible. The game is over when a monochromatic triangle is created. The online version of the game requires that the Player should colour each edge when it comes, before looki...

This paper concerns improper λ-colourings of graphs and focuses on the sizes of the monochromatic components (i.e., components of the subgraphs induced by the colour classes). Consider the following three simple operations, which should, heuristically, help reduce monochromatic component size: (a) assign to a vertex the colour that is least popular among its neighbours; (b) change the colours o...

We call the digraph D an m-coloured digraph if its arcs are coloured with m colours. If D is an m-coloured digraph and a ∈ A(D), colour(a) will denote the colour has been used on a. A path (or a cycle) is called monochromatic if all of its arcs are coloured alike. A γ-cycle in D is a sequence of vertices, say γ = (u0, u1, . . . , un), such that ui 6= uj if i 6= j and for every i ∈ {0, 1, . . . ...

We study the Orchard relation defined in [3] for generic configurations of points in the plane (also called order types). We introduce infinitesimally-close points and analyse the relation of this notion with the Orchard relation. The second part of the paper deals with monochromatic configurations (for the Orchard relation). We give the complete list of all monochromatic configurations up to 7...

In 1959, Goodman [9] determined the minimum number of monochromatic triangles in a complete graph whose edge set is 2-coloured. Goodman [10] also raised the question of proving analogous results for complete graphs whose edge sets are coloured with more than two colours. In this paper, for n sufficiently large, we determine the minimum number of monochromatic triangles in a 3-coloured copy of K...

We show in this paper that in every 3-coloring of the edges of K all but o(n) of its vertices can be partitioned into three monochromatic cycles. From this, using our earlier results, actually it follows that we can partition all the vertices into at most 17 monochromatic cycles, improving the best known bounds. If the colors of the three monochromatic cycles must be different then one can cove...

A factorisation x = u 1 2 ? $x u_1 u_2 \cdots$ of an infinite word $x$ on alphabet X $X$ is called ‘monochromatic’, for a given colouring the finite words ? $X^*$ , if each i $u_i$ same colour. Wojcik and Zamboni proved that periodic only every there monochromatic . On other hand, it follows from Ramsey's theorem that, any suffix having factorisation. ‘super-monochromatic’ k n $u_{k_1} u_{k_2} ...

conclusion the study data highlighted good value of iodine-based material decomposition images of spectral ct in assessment of both lipiodol deposition and residual cancer for follow-up of hcc patients previously treated with tace. background it is critical to follow up hepatocellular carcinoma (hcc) after transcatheter arterial chemoembolization (tace) in clinical practice. computed tomography...

The aim of this study was to investigate the performance of monochromatic images of spectral computed tomographic (CT) in the visualization of the pancreatic arteries compared with polychromatic CT images. We conducted a case-control study in a group of 26 consecutive patients with monochromatic CT and contrasted the results against a control group of 26 consecutive patients with polychromatic ...

An m-colored digraph is a digraph whose arcs are colored with m colors. A directed path is monochromatic when its arcs are colored alike. A set S ⊆ V (D) is a kernel by monochromatic paths whenever the two following conditions hold: 1. For any x, y ∈ S, x 6= y, there is no monochromatic directed path between them. 2. For each z ∈ (V (D)− S) there exists a zS-monochromatic directed path. In this...