An edge colouring of a graph is said to be an r-local colouring if the edges incident to any vertex are coloured with at most r colours. Generalising a result of Bessy–Thomassé and others, we prove that the vertex set of any 2-locally coloured complete graph may be partitioned into two disjoint monochromatic cycles of different colours. Moreover, for any natural number r, we show that the verte...

For two vertices u and v in a graph G = (V,E), the detour distance D(u, v) is length of longest − path G. A called detour. subsets B V , D(A,B) defined as min{D(x, y) : x ∈ A, y B}. an A-B joining sets A,B ⊆ where B. vertex said to lie on if some A−B set S E edge-to-vertex every incident with edge or lies pair edges S. The number dn2(G) minimum order its any basis Graphs size q for which 2 are ...

We further develop the 0/1 ILP formulation of Lee for edge coloring where colors are encoded in binary. With respect to that formulation, our main contributions are: (i) an efficient separation algorithm for general block inequalities, (ii) an efficient LP-based separation algorithm for stars (i.e., the all-different polytope), (iii) introduction of matching inequalities, and (iv) introduction ...

A coloring of the edges of Kn is constructed such that every copy of K4 has at least three colors on its edges. As n → ∞, the number of colors used is eO( √ log n ). This improves upon the previous probabilistic bound of O( √ n ) due to Erdős and Gyárfás.

the zagros fold-and-thrust belt is tectonically active and often has active faults with insensible and slow motions. determining the rate of movement and displacement in these faults requires very precise measurements. one of the measurement methods of fault movements is using geodetic and micro-geodetic studies. this research is focused on one of the active faults in the north of shiraz city, ...