A note on degree-constrained subgraphs

A Note on Degree-Constrained Star Subgraphs of Bipartite Graphs

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...

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...

Resource Constrained Project Scheduling with Material Ordering: Two Hybridized Meta-Heuristic Approaches (TECHNICAL NOTE)

Resource constrained project scheduling problem (RCPSP) is mainly investigated with the objective of either minimizing project makespan or maximizing project net present value. However, when material planning plays a key role in a project, the existing models cannot help determining material ordering plans to minimize material costs. In this paper, the RCPSP incorporated with the material order...

Conditions for families of disjoint k-connected subgraphs in a graph

In [Many disjoint dense subgraphs versus large k-connected subgraphs in large graphs with given edge density, Discrete Math. 309 (2009), 997–1000.], Böhme and Kostochka showed that every large enough graph with sufficient edge density contains either a kconnected subgraph of order at least r or a family of r vertex-disjoint k-connected subgraphs. Motivated by this, in this note we explore the l...