# Combinatorics and Graph Theory

## 1806 Submissions

 viXra:1806.0336 [pdf] submitted on 2018-06-22 07:08:11

### Independence of Clique Problems

Authors: Thinh Nguyen

A polynomial algorithm is “faster” than an exponential algorithm. As n grows an (exponential) always grows faster than nk (polynomial), i.e. for any values of a and k, after n> certain integer n0, it is true that an > nk. Even 2^n grows faster than n1000 at some large value of n. The former functions are exponential and the later functions are polynomial. It seems that for some problems we just may not have any polynomial algorithm at all (as in the information theoretic bound)! The theory of NPcompleteness is about this issue, and in general the computational complexity theory addresses it.
Category: Combinatorics and Graph Theory

 viXra:1806.0238 [pdf] submitted on 2018-06-18 00:11:02

### Linear Programming Solves Biclique Problems, Flaws in Literature Proof

Authors: Thinh D. Nguyen

The study of perebor dates back to the Soviet-era mathematics, especially in the 1980s . Post-Soviet mathematicians have been working on many problems in combinatorial optimization. One of them is Maximum Edge Biclique Problem (MBP). In , the author proves that MBP is NP-complete. In this note, we give a polynomial time algorithm for MBP by using linear programming (LP). Thus, some flaw needs to be found in Peeter's work. We leave this to the community.
Category: Combinatorics and Graph Theory

 viXra:1806.0179 [pdf] submitted on 2018-06-14 03:30:42

### Exact Weight Perfect Matching of Bipartite Graph Problem Simplified

Authors: Thinh D. Nguyen

The study of perebor dates back to the Soviet-era mathematics, especially in the 1980s . Post-Soviet mathematicians has been working on many problems in combinatorial optimization. One of them is Exact Weight Perfect Matching of Bipartite Graph (EWPM).This particular problem has been thoroughly considered by , , . In this note, we give a simpler proof about the solvability of EWPM.
Category: Combinatorics and Graph Theory

 viXra:1806.0065 [pdf] submitted on 2018-06-05 08:32:38

### Proof of the Goldbach Conjecture

Authors: Zhuwenhao

This proves that any even number larger than 2 can be written as the sum of two prime Numbers, also known as the "goldbach conjecture" or "goldbach conjecture about the even" is in the test for any greater than or equal to 6 even conform to guess the number of prime Numbers, accidentally discovered the prime Numbers of "additionality" and further expansion of verification.This article does not focus on the functional expressions of prime Numbers themselves, but takes a different approach to prove that all even Numbers can be composed of two prime Numbers
Category: Combinatorics and Graph Theory

 viXra:1806.0049 [pdf] submitted on 2018-06-06 02:48:22

### CSP Solver and Capacitated Vehile Routing Problem

Authors: Thinh D. Nguyen