## Abstract An __n__‐vertex graph is called pancyclic if it contains a cycle of length __t__ for all 3≤__t__≤__n__. In this article, we study pancyclicity of random graphs in the context of resilience, and prove that if __p__>__n__^−1/2^, then the random graph __G__(__n, p__) a.a.s. satisfies the f
Subgraphs of graphs, I
✍ Scribed by Paul A. Catlin
- Publisher
- Elsevier Science
- Year
- 1974
- Tongue
- English
- Weight
- 737 KB
- Volume
- 10
- Category
- Article
- ISSN
- 0012-365X
No coin nor oath required. For personal study only.
✦ Synopsis
&et G' and H aphs on p vertices. We give a suffictent Londition, based f the verrices of G and the maximum degree of t w vertices of ff' for Throughout this paper, all graphs considered are finite and simpl;. The C&~WP of a vertex v in the graph G is denoted deg<; (v). The vertex set of G is dencted V(G). e say that a graph H can be embedded into h G if there is an injec V(H) -+ V(G) such that if v and acent in H, then w v) and R(W) are adjaceA in 9;. Given graphs WC give a sufficient condition for the existence of an emb e notation G(1, X) s r a bipartite graph wit!-1
📜 SIMILAR VOLUMES
## Abstract Cartesian products of complete graphs are known as Hamming graphs. Using embeddings into Cartesian products of quotient graphs we characterize subgraphs, induced subgraphs, and isometric subgraphs of Hamming graphs. For instance, a graph __G__ is an induced subgraph of a Hamming graph i
## Abstract We shall prove that if __L__ is a 3‐chromatic (so called “forbidden”) graph, and —__R__^__n__^ is a random graph on __n__ vertices, whose edges are chosen independently, with probability __p__, and —__B__^__n__^ is a bipartite subgraph of __R__^__n__^ of maximum size, —__F__^__n__^ is a
## An emhdding of graph G into graph N is by definition an isomorphism OI G onto a subgraph of H. It is shown in this paper that every unicycle V embeds in its line-graph L(V), and that every other connected graph that embeds in its own line-graph may be constructed from such an embedded unicycle
## Abstract Given a “forbidden graph” __F__ and an integer __k__, an __F‐avoiding k‐coloring__ of a graph __G__ is a __k__‐coloring of the vertices of __G__ such that no maximal __F__‐free subgraph of __G__ is monochromatic. The __F‐avoiding chromatic number__ __ac__~__F__~(__G__) is the smallest i