We prove that if G is the line graph of a multigraph, then the chromatic number χ(G) of G is at most max {

A graph G is pluperfect if one can add new multiple edges to obtain a multi graph M satisfying: (1) G spans M, (2) the degrees of the nodes of M are consecutive integers, (3) G and M have the same minimum degree. Our purpose is to display several families of pluperfect graphs in order to L Introduction My good friends Mehdi Behzad and Gary Chartrand wrote a note [1] titled "No graph is perfect"...

Proofs of NP-hardness of the maximum k-intersection, edge labeled multigraph max capacity k-path, and max factor k-gcd problems are presented.

The result announced in the title is proved. A new proof of the total 6-colorability of any multigraph with maximum degree 4 is also given.

The Platonic graphs πn arise in several contexts, most simply as a quotient of certain Cayley graphs associated to the projective special linear groups. We show that when n = p is prime, πn can be viewed as a complete multigraph in which each vertex is itself a wheel on n + 1 vertices. We prove a similar structure theorem for the case of an arbitrary prime power. These theorems are then used to...