Degree constrained subgraphs

Decompositions to Degree-Constrainded Subgraphs Are Simply Reducible to Edge-Colorings

The degree-constrained subgraphs decomposition problem, such as an f-coloring, an f-factorization, and a [ g, f ]-factorization, is to decompose a given graph G=(V, E) to edge-disjoint subgraphs degree-constrained by integer-valued functions f and g on V. In this paper we show that the problem can be simply reduced to the edge-coloring problem in polynomial-time. That is, for any positive integ...

A Note on Degree-Constrained Star Subgraphs of Bipartite Graphs

On Decomposing Graphs of Large Minimum Degree into Locally Irregular Subgraphs

A locally irregular graph is a graph whose adjacent vertices have distinct degrees. We say that a graph G can be decomposed into k locally irregular subgraphs if its edge set may be partitioned into k subsets each of which induces a locally irregular subgraph in G. It has been conjectured that apart from the family of exceptions which admit no such decompositions, i.e., odd paths, odd cycles an...

Generation and analysis of networks with a prescribed degree sequence and subgraph family: higher-order structure matters

Designing algorithms that generate networks with a given degree sequence while varying both subgraph composition and distribution of subgraphs around nodes is an important but challenging research problem. Current algorithms lack control of key network parameters, the ability to specify to what subgraphs a node belongs to, come at a considerable complexity cost or, critically, sample from a lim...

Ignasi SAU VALLS Optimization in Graphs under Degree Constraints Application to Telecommunication Networks

The first part of this thesis is devoted to traffic grooming, which is a central problem in optical networks. It refers to packing low-rate signals into higher-speed streams, in order to improve bandwidth utilization and reduce the network cost. The objective is to minimize the number of Add-Drop Multiplexers (ADMs), which are devices that insert/extract low-rate traffic to/from a high-speed st...

Grooming traffic to minimize load

Grooming traffic in optical networks can be formulated as partitioning the edges of a graph into subgraphs each having at most a specified number c of edges; a typical objective is to minimize the sum over all subgraphs of the vertices of nonzero degree (the drop cost). In practice, however, one may be constrained so that each vertex has nonzero degree in a limited number of different subgraphs...