Degree Sequen es of Optimally Edge-Conne ted Multigraphs

An Efficient Algorithm for Edge-Coloring Series-Parallel Multigraphs

Many combinatorial problems can be efficiently solved for series-parallel graphs or partial k-trees. The edge-coloring problem is one of a few combinatorial problems for which no efficient algorithms have been obtained for series-parallel multigraphs. This paper gives an algorithm which optimally edge-colors a given series-parallel multigraph in time O([V[z~), where V is the set of vertices and...

Degree sequence conditions for maximally edge-connected graphs depending on the clique number

Theorem 1 was the starting point for many other suÆ ient onditions for = Æ. Lesniak [9℄ weakened the ondition Æ bn=2 to deg(u) + deg(v) n for all pairs of nonadja ent verti es u and v in G. Plesn k [10℄ showed that every graph of diameter 2 satis es = Æ and thus generalized Lesniak's result. Improvements of Plesn k's result an be found in Plesn k, Zn am [11℄ and Dankelmann, Volkmann [4℄ (see al...

Learning High-Degree Sequen es in a Linear Network

R O M A

We investigate the problem of omputing the types of the relationships between Internet Autonomous Systems. We refer to the model introdu ed in [6, 17℄ that bases the dis overy of su h relationships on the analysis of the AS paths extra ted from the BGP routing tables. We hara terize the time omplexity of the above problem, showing both NPompleteness results and eÆ ient algorithms for solving sp...

An NC Parallel Algorithm for Edge-Coloring Series-Parallel Multigraphs

Many combinatorial problems can be efficiently solved in parallel for series]parallel multigraphs. The edge-coloring problem is one of a few combinatorial problems for which no NC parallel algorithm has been obtained for series]parallel multigraphs. This paper gives an NC parallel algorithm for the Ž . Ž . problem on series]parallel multigraphs G. It takes O log n time with O Dnrlog n processor...