2004 Fiscal Year Final Research Report Summary
Embedding and Partition of Graphs
| Project/Area Number |
14540134
|
|---|
| Research Category |
Grant-in-Aid for Scientific Research (C)
|
| Allocation Type | Single-year Grants |
|---|
| Section | 一般 |
|---|
| Research Field |
General mathematics (including Probability theory/Statistical mathematics)
|
|---|
| Research Institution | HIROSHIMA UNIVERSITY (2003-2004)
Keio University (2002) |
|---|
Principal Investigator |
ENOMOTO Hikoe Hiroshima University, Graduate School of Science, Professor, 大学院・理学研究科, 教授 (00011669)
|
|---|
| Co-Investigator(Kenkyū-buntansha) |
OTA Katsuhiro Keio University, Faculty of Science and Technology, Professor, 理工学部, 教授 (40213722)
MATSUMOTO Makoto Hiroshima University, Graduate School of Science, Professor, 大学院・理学研究科, 教授 (70231602)
|
|---|
| Project Period (FY) |
2002 – 2004
|
| Keywords | graph / cycle / factor / decree condition / independence number / connectivity |
|---|
| Research Abstract |
(1)In 1997, Brandt and others proved that a graph G of order at least 4k and the degree sum of nonadjacent vertices at least |V(G)| can be partitioned into k disjoint cycles. This result is generalized in several ways. We weakened the degree sum assumption to |V(G)|-k+1 by allowing degenerated cycles (edges and isolated vertices). We also obtained sufficient conditions on the minimum degree to assure that each cycle passes through a specified vertex. We also solved the problem in which each cycle passes through a specified vertex or a specified edge. Furthermore, we solved the problem for bipartite graphs.
(2)Erdos-Chvatal theorem says that if the independence number is not larger than the connectivity, the graph contains a Hamiltonian cycle. We generalized this result to the existence of a long cycle.
(3)We investigated the maximum order of a graph without k disjoint cycles and the independence number is at most α.
(4)We proved that if G is an (mg+m-1,mf-m+1)-graph and if k≦g(x)≦f(x) for any vertex x of G,G can be factorized into (g,f)-factors in which each factor contains k specified edges.
|
