Multidesigns for a Graph Pair of Order 6

Oral presentation abstract

Decomposing Complete Graphs into a Graph Pair of Order 6

Firstly, a graph G consists of a vertex set V (G), and an edge set E (G) of endpoints which relate two vertices with each edge. Also, a decomposition of a graph is a list of subgraphs such that each edge appears in exactly one subgraph in the list. In the field of graph theory, graph decomposition is an active field of research. A graph pair is a pair of graphs on the same vertex set whose union is the complete graph. Abueida and Daven studied decompositions of complete graphs into graph-pairs of order four and five. We are extending their results by investigating which complete graphs decompose into a specific graph pair of order 6

A Look at Multi-Decompositions of Complete Graphs into Graph Pairs of Order 4

Firstly, a graph G consists of a vertex set V (G), and an edge set E (G) of endpoints which relate two vertices with each edge. Also, a decomposition of a graph is a list of subgraphs such that each edge appears in exactly one subgraph in the list. In the field ofgraph theory, graph decomposition is an active field of research. One type of decomposition is graph pairs. A graph pair is a pair of graphs on the same vertex set whose union is the complete graph. Abueida and Daven studieddecompositions of complete graphs into graph-pairs of order four. In their proof, they left a small part to the readers. We will complete this proof

A Controllable Model of Grounded Response Generation

Current end-to-end neural conversation models inherently lack the flexibility to impose semantic control in the response generation process, often resulting in uninteresting responses. Attempts to boost informativeness alone come at the expense of factual accuracy, as attested by pretrained language models' propensity to "hallucinate" facts. While this may be mitigated by access to background knowledge, there is scant guarantee of relevance and informativeness in generated responses. We propose a framework that we call controllable grounded response generation (CGRG), in which lexical control phrases are either provided by a user or automatically extracted by a control phrase predictor from dialogue context and grounding knowledge. Quantitative and qualitative results show that, using this framework, a transformer based model with a novel inductive attention mechanism, trained on a conversation-like Reddit dataset, outperforms strong generation baselines.Comment: AAAI 202