Thomassen [9] conjectured that for all natural numbers k > 0 and m, every graph of minimum degree k + 1 contains a cycle of length congruent to 2m modulo k. We prove that this ...
We describe efficient algorithms for finding even cycles in undirected graphs. Our main results are the following: (i) For every k 2, there is an O(V 2) time algorithm that decide...
We prove that for every c > 0 there exists a constant K = K(c) such that every graph G with n vertices and minimum degree at least cn contains a cycle of length t for every even...
A graph G is k-linked if G has at least 2k vertices, and for every sequence x1, x2, . . . , xk, y1, y2, . . . , yk of distinct vertices, G contains k vertex-disjoint paths P1, P2,...