## Abstract We show that every 1βtough graph __G__ on __n__ β₯ 3 vertices with Ο~3~β§ __n__ has a cycle of length at least min{__n, n__ + (Ο~3~/3 ) β Ξ± + 1}, where Ο~3~ denotes the minimum value of the degree sum of any 3 pairwise nonadjacent vertices and Ξ± the cardinality of a miximum independent se
Circumference of Graphs with Bounded Degree
β Scribed by Chen, Guantao; Xu, Jun; Yu, Xingxing
- Book ID
- 118181275
- Publisher
- Society for Industrial and Applied Mathematics
- Year
- 2004
- Tongue
- English
- Weight
- 414 KB
- Volume
- 33
- Category
- Article
- ISSN
- 0097-5397
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π SIMILAR VOLUMES
## Abstract Let __C__ be a longest cycle in the 3βconnected graph __G__ and let __H__ be a component of __G__βββ__V__(__C__) such that |__V__(__H__)|ββ₯β3. We supply estimates of the form |__C__|ββ₯β2__d__(__u__)β+β2__d__(__v__)βββΞ±(4ββ€βΞ±ββ€β8), where __u__,__v__ are suitably chosen nonβadjacent verti
Let ex\*(D;H) be the maximum number of edges in a connected graph with maximum degree D and no induced subgraph H; this is finite if and only if H is a disjoint union of paths. If the largest component of such an H has order m, then ex\*(D;H) = O(D2ex\*(D;Pm)). Constructively, ex\*(D;qPm) = O(qD2ex\
## Abstract Let __ex__ \* (__D__; __H__) denote the maximum number of edges in a connected graph with maximum degree __D__ and no induced subgraph isomorphic to __H.__ We prove that this is finite only when __H__ is a disjoint union of paths,m in which case we provide crude upper and lower bounds.