Grunnleggende konsepter
Average hereditary graphs have interesting properties, including improved chromatic number bounds and NP-hardness in graph 3-coloring.
Sammendrag
This paper introduces average hereditary graphs, explores their properties, and proves the NP-hardness of graph 3-coloring within this class. The analysis includes new upper bounds for the chromatic number based on average degree, construction methods, closure under binary operations, and algebraic properties as a commutative monoid. Acknowledgments are made to mentors for guidance.
Statistikk
d(G(φ)) = 3 * ((8C + L + 2) / (6C + L + 3))
MAD(G) ≤ ∆(G)
MAD(G) can be computed in polynomial time by Goldberg's algorithm.
Sitater
"Most graphs that occur in usual graph theory applications belong to this class." - Syed Mujtaba Hassan & Shahid Hussain
"Graph coloring is famously NP-complete." - Authors
"Graph join operation is associative." - Theorem 3