The search session has expired. Please query the service again.
The search session has expired. Please query the service again.
Jochen Harant, Stanislav Jendrol', Hansjoachim Walther (2008)
Discussiones Mathematicae Graph Theory
Similarity:
For a 3-connected planar graph G with circumference c ≥ 44 it is proved that G has a cycle of length at least (1/36)c+(20/3) through any four vertices of G.
David Auger, Irène Charon, Olivier Hudry, Antoine Lobstein (2010)
Discussiones Mathematicae Graph Theory
Similarity:
We consider a simple, undirected graph G. The ball of a subset Y of vertices in G is the set of vertices in G at distance at most one from a vertex in Y. Assuming that the balls of all subsets of at most two vertices in G are distinct, we prove that G admits a cycle with length at least 7.
Yang Wang, Weifan Wang, Jiangxu Kong, Yiqiao Wang (2024)
Czechoslovak Mathematical Journal
Similarity:
It was known that the vertex set of every planar graph can be partitioned into three forests. We prove that the vertex set of a planar graph without chordal 5-cycles can be partitioned into two forests. This extends a result obtained by Raspaud and Wang in 2008.
Gould, Ronald, Łuczak, Tomasz, Schmitt, John (2006)
The Electronic Journal of Combinatorics [electronic only]
Similarity:
Tomoki Yamashita (2007)
Discussiones Mathematicae Graph Theory
Similarity:
A cycle C is a vertex-dominating cycle if every vertex is adjacent to some vertex of C. Bondy and Fan [4] showed that if G is a 2-connected graph with δ(G) ≥ 1/3(|V(G)| - 4), then G has a vertex-dominating cycle. In this paper, we prove that if G is a 2-connected bipartite graph with partite sets V₁ and V₂ such that δ(G) ≥ 1/3(max{|V₁|,|V₂|} + 1), then G has a vertex-dominating cycle.
Vasil Jacoš, Stanislav Jendroľ (1974)
Matematický časopis
Similarity:
Wojciech Wide (2017)
Discussiones Mathematicae Graph Theory
Similarity:
A graph G on n vertices is said to be pancyclic if it contains cycles of all lengths k for k ∈ {3, . . . , n}. A vertex v ∈ V (G) is called super-heavy if the number of its neighbours in G is at least (n+1)/2. For a given graph H we say that G is H-f1-heavy if for every induced subgraph K of G isomorphic to H and every two vertices u, v ∈ V (K), dK(u, v) = 2 implies that at least one of them is super-heavy. For a family of graphs H we say that G is H-f1-heavy, if G is H-f1-heavy for...
Ladislav Stacho (2002)
Mathematica Slovaca
Similarity:
Fatima Affif Chaouche, Carrie G. Rutherford, Robin W. Whitty (2015)
Discussiones Mathematicae Graph Theory
Similarity:
It is known that Θ(log n) chords must be added to an n-cycle to produce a pancyclic graph; for vertex pancyclicity, where every vertex belongs to a cycle of every length, Θ(n) chords are required. A possibly ‘intermediate’ variation is the following: given k, 1 ≤ k ≤ n, how many chords must be added to ensure that there exist cycles of every possible length each of which passes exactly k chords? For fixed k, we establish a lower bound of ∩(n1/k) on the growth rate.
Yoshimi Egawa, Mikio Kano, Zheng Yan (2014)
Discussiones Mathematicae Graph Theory
Similarity:
A spanning subgraph F of a graph G is called a star-cycle factor of G if each component of F is a star or cycle. Let G be a graph and f : V (G) → {1, 2, 3, . . .} be a function. Let W = {v ∈ V (G) : f(v) = 1}. Under this notation, it was proved by Berge and Las Vergnas that G has a star-cycle factor F with the property that (i) if a component D of F is a star with center v, then degF (v) ≤ f(v), and (ii) if a component D of F is a cycle, then V (D) ⊆ W if and only if iso(G − S) ≤ Σx∈S...