A sufficient condition for a pair of sequences to be bipartite graphic

We present a sufficient condition for a pair of finite integer sequences to be degree sequences of a bipartite graph, based only on the lengths of the sequences and their largest and smallest elements.Comment: 5 page

A Sufficient Condition for Graphic Sequences with Given Largest and Smallest Entries, Length, and Sum

We give a sufficient condition for a degree sequence to be graphic based on its largest and smallest elements, length, and sum. This bound generalizes a result of Zverovich and Zverovich

Symmetric Bipartite Graphs and Graphs with Loops

We show that if the two parts of a finite bipartite graph have the same degree sequence, then there is a bipartite graph, with the same degree sequences, which is symmetric, in that it has an involutive graph automorphism that interchanges its two parts. To prove this, we study the relationship between symmetric bipartite graphs and graphs with loops.Comment: arXiv admin note: substantial text overlap with arXiv:1302.365

Automated construction of variable density navigable networks in a 3D indoor environment for emergency response

Widespread human-induced or natural threats on buildings and their users have made preparedness and quick response as crucial issues for saving human lives. Available information about an emergency scene, e.g. the building structure, material and trapped people helps for decision-making and organizing rescue operations. The ability to evaluate potential scenarios for human evacuation, and then identifying the paths of egress during an emergency is critical for rescue and emergency services. Good quality models supporting real, or near-real, time decision-making and allowing the implementation of automated methods are highly desirable. In this paper, we propose a new automated method for deriving a navigable network in a 3D indoor environment, including a full 3D topological model which may be used not only for standard navigation but also for finding alternative egress routes and simulating phenomena associated with disasters such as fire spread and heat transfer