摘要

組合數學與圖論是一門研究離散物件的科學。隨著電腦科學的迅速發展，組合數學 與圖論的研究得到人們日益的重視。組合數學與圖論不僅在電腦科學、通訊科學、編碼和密 碼學、物理、化學、生物學等學科中有重要應用，還在企業管理、交通運輸、戰爭指揮、金 融分析等領域有直接應用。

本演講主要圍繞組合與圖論中的幾個經典問題：四色問題、七橋問題、漢米爾頓圈 問題、最短路問題、拉姆齊數、鴿籠原理、斐波那契數列。具體介紹這些問題的提出與引入 、歷史與現狀、發展與應用等。

Abstract

Combinatorics and graph theory is the science of studying discrete objects. With the rapid development of computer science, the study of combinatorics and graph theory becomes more and more important. Besides important applications in computer science; communication; coding and cryptography; physics; chemistry; and biology, it can be directly applied to enterprise management; transportation; war command; and financial analysis.

In this talk, we shall focus on classical problems in combinatorics and graph theory including the four color problem; the seven bridges problem; Hamiltonian cycle problem; the shortest path problem; Ramsay number; pigeonhole principle; and Fibonacci sequence. We shall introduce their backgrounds, history, development and applications.