A new generalization of subgraphs whose edges have distinct colors and its applications to BH conjecture

2015 Fiscal Year Final Research Report

• Project/Area Number: 24740068
• Research Category: Grant-in-Aid for Young Scientists (B)
• Allocation Type: Multi-year Fund
• Research Field: General mathematics (including Probability theory/Statistical mathematics)
• Research Institution: Kochi University
• Principal Investigator: Suzuki kazuhiro 高知大学, 教育研究部自然科学系, 助教 (50514410)
• Project Period (FY): 2012-04-01 – 2016-03-31
• Keywords: グラフ理論 / 離散幾何学 / 全域木 / 辺着色 / 辺彩色 / 異色全域木 / 異色部分グラフ

Outline of Final Research Achievements

A subgraph whose edges have distinct colors is called a heterochromatic subgraph. We define a (g,f)-chromatic subgraph as a subgraph having at least g(c) and at most f(c) edges colored with c for any color c, where g and f are functions from a color set to the set of non-negative integers. In this research, we studied conditions for existence of a (g,f)-chromatic subgraph in edge-colored graphs, and we got the following results.
(1) We got a necessary and sufficient condition for existence of a (g,f)-chromatic subgraph in edge-colored graphs. (2) We studied heterochromatic subgraphs with some upper bound of maximum degree. (3) We generalized some previous results on heterochromatic subgraphs. (4) We got a sufficient condition for existence of a spanning k-tree in bipartite graphs. (5) We got a Lemma for balanced partition of a sequence of colored elements.

Free Research Field

グラフ理論、離散幾何学