On Graphs Satisfying a Local Ore-Type

Abstract

For an integer i, a graph is called an L,-graph if, for each triple of vertices u, u , w with d(u, U ) = 2 and w E N(u) n N ( u ) , d(u) + d(u) 2 IN(u) u N(u) U N(w)l i. Asratian and Khachatrian proved that connected Lo-graphs of order a t least 3 are hamiltonian, thus improving Ore's Theorem. All K1,3-free graphs are L1-graphs, whence recognizing… (More)

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