9 research outputs found
An alternative proof of the nowhere-zero 6-flow theorem
The nowhere-zero 6-flow theorem of Seymour is proven by construction
Construction of cycle double covers for certain classes of graphs
We introduce two classes of graphs, Indonesian graphs and -doughnut graphs. Cycle double covers are constructed for these classes. In case of doughnut graphs this is done for the values and 4
Restricted Size Ramsey Number for Path of Order Three Versus Graph of Order Five
Let and be simple graphs. The Ramsey number for a pair of graph and is the smallest number such that any red-blue coloring of edges of contains a red subgraph or a blue subgraph . The size Ramsey number for a pair of graph and is the smallest number such that there exists a graph with size satisfying the property that any red-blue coloring of edges of contains a red subgraph or a blue subgraph . Additionally, if the order of in the size Ramsey number is , then it is called the restricted size Ramsey number. In 1983, Harary and Miller started to find the (restricted) size Ramsey number for any pair of small graphs with order at most four. Faudree and Sheehan (1983) continued Harary and Miller\u27s works and summarized the complete results on the (restricted) size Ramsey number for any pair of small graphs with order at most four. In 1998, Lortz and Mengenser gave both the size Ramsey number and the restricted size Ramsey number for any pair of small forests with order at most five. To continue their works, we investigate the restricted size Ramsey number for a path of order three versus connected graph of order five