Review of erdös on graphs: his legacy of unsolved problems by Fan Chung and Ron Graham

A classical result of Chvatal and Erdos says that the graph G with connectivity @k(G) not less than its independence number @a(G) (i.e. @k(G)>=@a(G)) is Hamiltonian. In this paper, we show that the 2-connected graph G with @k(G)>=@a(G)-1 is one of the ...

For a graph H, let $$\alpha (H)$$ź(H) and $$\alpha ^{\prime }(H)$$źź(H) denote the independence number and the matching number, respectively. Let $$k\ge 2$$kź2 and $$r>0$$r>0 be given integers. We prove that if H is a k-connected claw-free graph with $$\...

The Fano plane is the unique linear 3-uniform hypergraph on seven vertices and seven hyperedges. It is known that, for all $n \geq 8$, the balanced complete bipartite 3-uniform hypergraph on $n$ vertices, denoted by $B_n$, is the 3-uniform hypergraph on $...