On the optimum graph of strong edge coloring conjecture

In our approach, the original network is decomposed into a set of smaller subnetworks to be processed, based on the concept of edge coloring and numbering combined with network topology.

The problem is Abstracted as an edge coloring problem of multi-graphs.

Supposing Г to be a 4-regtilar connected Cayley graph on an abelian group of odd order, the edge-coloring problem ofГ-{e1,e2 } is discussed in this paper,where e1, e2 are two arbitrary edges of Г.

Given a simple graph G,an edge-coloring of G with colors 1,2,3,… is called consecutive if the colors represented at each vertex form an interval of integers.

Given a simple graph G, an edge-coloring of G with colors 1,2,3 .

The determination of pefext matchings of a complete graph K_(4n) on the basic of △(G′)-edge colouring;

A(λ,β)-flaw k-edge colouring of a connected graph G=(V,E) is a mapping from E to {1,2,…,k} if there is a smallest integer β≥1 such that for every colour j∈{1,2,…,β} there is at least a vertex uj∈V(G)that is incident with λ edges coloured by colour j,and for each color l∈{β+1,…,k} no two edges incident with any vertex v∈V(G)receive the colour l.

This paper studies the referee assignment in the course of a single-recycling game by means of theory of edge-colouring and total colouring of graph and gives the optimal results.

In 1985,the famous graph theory expert Erds and Neetil ilconjectured that strong edge-coloring number of a graph is bounded above by 5/4Δ2 when Δ is even and 1/4(5Δ2-2Δ+1) when Δ is odd.