A vertex cover with chorded 4-cycles
β Scribed by Yun Shu Gao; Guo Jun Li; Jin Yan
- Publisher
- Institute of Mathematics, Chinese Academy of Sciences and Chinese Mathematical Society
- Year
- 2011
- Tongue
- English
- Weight
- 218 KB
- Volume
- 27
- Category
- Article
- ISSN
- 1439-7617
No coin nor oath required. For personal study only.
π SIMILAR VOLUMES
## Abstract In this paper, we prove that every cycle plus a chord is graceful, thus answering a conjecture of R. Bodendiek, H. Schumacher, and H. Wegner.
## Abstract Let __k__ and __n__ be two integers such that __k__ β₯ 0 and __n__ β₯ 3(__k__ + 1). Let __G__ be a graph of order __n__ with minimum degree at least β(__n__ + __k__)/2β. Then __G__ contains __k__ + 1 independent cycles covering all the vertices of __G__ such that __k__ of them are triangl
## Abstract Given positive integers __n__ and __k__, let __g__~__k__~(__n__) denote the maximum number of edges of a graph on __n__ vertices that does not contain a cycle with __k__ chords incident to a vertex on the cycle. BollobΓ‘s conjectured as an exercise in [2, p. 398, Problem 13] that there e
## Abstract It is shown that the edges of a simple graph with a nowhereβzero 4βflow can be covered with cycles such that the sum of the lengths of the cycles is at most |__E__(__G__)| + |__V__(__G__)| β3. This solves a conjecture proposed by G. Fan.
## Abstract We give a structural description of the class π of graphs that do not contain a cycle with a unique chord as an induced subgraph. Our main theorem states that any connected graph in π is either in some simple basic class or has a decomposition. Basic classes are chordless cycles, cliqu