The 2-parallel chromatic index X" (8) is the minimum number of colours required to colour the blocks of a Steiner triple system 8 so that any two parallel blocks receive different colours. The value of X" (v) = min {X" (8) : 8 is an 8TS(v)} is determined for all admissible v.-It is further shown how the 2-parallel chromatic index is related to the independence number and a complete analysis for...

A graph G is locally irregular if adjacent vertices of G have distinct degrees. An edge colouring of G is locally irregular if each of its colours induces a locally irregular subgraph of G. The irregular chromatic index of G refers to the least number of colours used by a locally irregular edge colouring of G (if any). We propose a linear-time algorithm for determining the irregular chromatic i...

The paper studies edge-coloring of signed multigraphs and extends classical Theorems Shannon K\"onig to multigraphs. We prove that the chromatic index a multigraph $(G,\sigma_G)$ is at most $\lfloor \frac{3}{2} \Delta(G) \rfloor$. Furthermore, balanced $(H,\sigma_H)$ $\Delta(H) + 1$ with $\Delta(H)$ are characterized.

If G is a graph, a G-decomposition of a host graph H is a partition of the edges of H into subgraphs of H which are isomorphic to G. The chromatic index of a Gdecomposition of H is the minimum number of colors required to color the parts of the decomposition so that parts which share a common node get different colors. We establish an upper bound on the chromatic index and characterize those de...