Chromatic indices of finite affine & projective planes and their duals

Abstract

In this study, rather than transitioning directly from geometric structures to graph theory, we have derived several general results and theorems concerning the coloring of points and lines within affine and projective structures. We approached this topic through the lens of vertex and edge coloring concepts, pivotal subjects within graph theory. Our investigation sheds light on the intricate relationship between geometric structures and graph theory, providing a novel perspective on coloring methodologies. Extending the principles of vertex and edge coloring to affine and projective spaces, we uncover fundamental insights into the interplay between geometry and combinatorial mathematics.

Keywords

• Affine Plane
• Projective Plane
• Chromatic Index

Sonlu Afin & Projektif düzlemlerin ve duallerinin kromatik indisleri

Abstract

Bu çalışmada, doğrudan geometrik yapılardan graf teorisine geçiş yapmak yerine, afin ve projektif yapılardaki nokta ve doğruların renklendirilmesiyle ilgili birkaç genel sonuç ve teorem ürettik. Bu konuya, graf teorideki temel konular olan köşe ve kenar renklendirme kavramları merceğinden yaklaştık. Araştırmamız, geometrik yapılar ve graf teori arasındaki karmaşık ilişkiye ışık tutarak, renklendirme metodolojilerine yeni bir bakış açısı sağlıyor. Köşe ve kenar renklendirme ilkelerini afin ve projektif uzaylara genişleterek, geometri ve kombinatoryal matematik arasındaki etkileşime dair temel içgörüler ortaya çıkarıyoruz.

Keywords

• Afin Düzlem
• Projektif Düzlem
• Kromatik İndis

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