We consider edge-coloured complete graphs. A path or cycle Q is called properly coloured (PC) if any two adjacent edges of Q differ in colour. Our note is inspired by the followi...
Let k = (k1, . . . , kn) be a sequence of n integers. For an increasing monotone graph property P we say that a base graph G = ([n], E) is k-resilient with respect to P if for eve...
Sonny Ben-Shimon, Michael Krivelevich, Benny Sudak...
In 1993, Brualdi and Massey conjectured that every graph can be incidence colored with + 2 colors, where is the maximum degree of a graph. Although this conjecture was solved in ...
Using an improved backtrack algorithm with sophisticated pruning techniques, we revise previous observations correlating a high frequency of hard to solve Hamiltonian cycle instan...
Let G be the set of finite graphs whose vertices belong to some fixed countable set, and let ≡ be an equivalence relation on G. By the strengthening of ≡ we mean an equivalen...