Kenta Ozeki

Rainbow Generalizations of Ramsey Theory: A Survey

In this work, we collect Ramsey-type results concerning rainbow edge colorings of graphs.

A Degree Sum Condition Concerning the Connectivity and the Independence Number of a Graph

AbstractLet G be a graph and S ⊂ V(G). We denote by α(S) the maximum number of pairwise nonadjacent vertices in S. For x, y ∈ V(G), the local connectivity κ(x, y) is defined to be the maximum number of internally-disjoint paths connecting x and y in G. We define

Hamiltonian cycles in bipartite quadrangulations on the torus

kappa(S)=min{kappa(x,y) : x,y inn S,xnot=y}

Long cycles in graphs without hamiltonian paths

. In this paper, we show that if κ(S) ≥xa03 and

A simple algorithm for 4-coloring 3-colorable planar graphs

sum_{i=1}^4 d_{G}{(x_i)} ge |V(G)|+kappa(S)+alpha (S)-1

A k-tree containing specified vertices

for every independent set {x1, x2, x3, x4} ⊂ S, then G contains a cycle passing through S. This degree condition is sharp and this gives a new degree sum condition for a 3-connected graph to be hamiltonian.