Combinatorics and Graph Theory

2305 Submissions

[3] viXra:2305.0126 [pdf] replaced on 2025-02-17 09:22:42

Novel Proof of the Four-Colour Theorem

Authors: Henri Caillaud
Comments: 23 Pages.

HAKEN and APPEL showed in their famous demonstration that the configuration consisting of two neighboring countries each having five neighbors was inevitable and irreducible. The present demonstration proposes a reduction of this configuration.
Category: Combinatorics and Graph Theory

[2] viXra:2305.0040 [pdf] submitted on 2023-05-06 01:46:21

An Elementary Solution of the Four-color Conjecture

Authors: Chongxi Yu
Comments: 3 Pages.

The four-color conjecture ( Guthrie's problem after F. Guthrie) is divided into 5 simple groups, every region is shared a common boundary with 1, 2, 3, 4, and unlimited regions sharing a common boundary (other than a single point) do not share the same color to make the problem much simpler and clearer, The four-color theorem is solved perfectly by using these simpler models.
Category: Combinatorics and Graph Theory

[1] viXra:2305.0003 [pdf] submitted on 2023-05-02 00:54:47

A Probabilistic Proof of the Multinomial Theorem Following the Number $a_n^p$

Authors: Atsu Dekpe
Comments: 3 Pages.

In this note, we give an alternate proof of the multinomial theorem following the number $ A_n^p $ using probabilistic approach. Although the multinomial theorem following the number $ A_n^p$ is basically a combinatorial result, our proof may be simple for a student familiar with only basic probability concepts.
Category: Combinatorics and Graph Theory