January 23, 2014 - A graph is said to be H^*-connected if it is either Hamilton-connected or Hamilton-laceable. S. Wagon (pers. comm., May. 20, 2013; Dupuis and Wagon 2014) conjecture that all connected vertex-transitive graphs are H^*-connected with the following ...

H. (As usual, χ(H) denotes the chromatic number of H). The exact statement of the result is the ... lemmas that are used in the proof. A short outline of the proof is presented in section 3. The proof · itself is described in detail in section 4. The tightness of the results, their algorithmic aspects and · some concluding remarks and open problems are discussed in the final section. ... cover almost all of the vertices of a (large) graph L with vertex disjoint copies of a (small) graph

The method of associating an oriented H-category to a graph defines a functor: Γ : Grph · −→ · Hcat · (5) Γ · 7→ · Γ(Γ) := HΓ . We can now introduce the inverse of this construction. H-Categories and Graphs · 6 · 3.3. Oriented graphs from oriented H-categories.

Let H be a loopless graph with k edges and δ(H) ≥2.

Recall that a graph is k-linked if for every list of 2k vertices fs1; . . . ; sk; t1; . . . ; tkg, there exist internally disjoint paths P1; . . . ; Pk such that each Pi is an · si; ti-path. From the definitions of k-linked and H-linked graphs, we immediately

A graph G is k-linked if for any ordered subset of 2k vertices S = {s1, t1, . . . , sk, tk} there exist disjoint paths P1, . . . , Pk such that for each i, Pi is an si −ti path. We will · 1991 Mathematics Subject Classification. 05C38, 05C83. Key words and phrases. H-linked Graph, k-linked ...

Given a fixed multigraph H, possibly containing loops, with $V(H) = \{h_1,\ldots,h_m\}$, we say that a graph G is H‐linked if for every choice of m vertices $v_1,\ldots,v_m$ in G, there exists a subdivision of H in G such that $v_i$ is the ...

1 week ago - Subsequently, Kelly, Kühn, and Osthus showed that such oriented graphs {are also arbitrary $ H $-linked, where $H$ is a loop}. Motivated by these results, we establish a minimum semi-degree condition for arbitrary $ H $-linked oriented graphs: there exists $ n_0 = n_0(h,q) $ such that every oriented graph $ D $ of order $ n \geq n_0 $ with $\delta^0(D) \geq \frac{3n + 3h + 3q - 5}{8}$ is arbitrary $ H $-linked; specifically, if $H$ is a loop, this holds under the weaker condition $\delta^0(D) \geq \frac{3n - 4}{8}$. The result provides an oriented graph analogue of Wang's conjecture on cycle-factors in graphs [J.

January 28, 2010 - "The" H graph is the tree on 6 vertices illustrated above. It is implemented in the Wolfram Language as GraphData["HGraph"]. The term "H-graph" is also used to refer to a graph expansion with the 6-vertex H graph as its base (e.g., Horton and ...

For a fixed multigraph H, possibly containing loops, with V(H)={h1, . . . , h k }, we say a graph G is H-linked if for every choice of k vertices v1, . . . , v k in G, there exists a subdivision of H in G such that v i represents h i (for all i). ...

November 28, 2016 - Abstract For graphs G and H, an H-coloring of G is a map from the vertices of G to the vertices of H that preserves edge adjacency. We consider the following extremal enumerative question: for a gi...

January 1, 2014 - ... For a connected graph H of ... as that graph whose vertices are the edges of G and where two vertices are adjacent if and only if the corresponding edges of G are adjacent and belong to a common copy of H....

Theorem 2.2 Let H ∼= P6. Then the sequence {HLk(G)} converges if and only · if each component of G is isomorphic to Cn for some n ≥6 or each component is · isomorphic to one of the graphs given below, namely, G1, G2, Aj, Bj, Ci,j.

April 27, 2022 - The H-join of a family of graphs G={G1,…,Gp}, also called generalized composition, H[G1,…,Gp], where all graphs are undirected, simple and finite, is …

1 week ago - The notion of "graph isomorphism" allows us to distinguish graph properties inherent to the structures of graphs themselves from properties associated with graph representations: graph drawings, data structures for graphs, graph labelings, etc. For example, if a graph has exactly one cycle, ...

2 weeks ago - It can be desirable to study hypergraphs where all hyperedges have the same cardinality; a k-uniform hypergraph is a hypergraph such that all its hyperedges have size k. (In other words, one such hypergraph is a collection of sets, each such set a hyperedge connecting k nodes.) So a 2-uniform hypergraph is a graph, a 3-uniform hypergraph is a collection of unordered triples, and so on.

May 29, 2003 - Chartrand, Kaugars and Lick proved that every critically h-connected graph contains a vertex of degree not exceeding 32h−1. We prove here that there a…

February 11, 2021 - Abstract:The $H$-join of a family of graphs $\mathcal{G}=\{G_1, \dots, G_p\}$, also called the generalized composition, $H[G_1, \dots, G_p]$, where all graphs are undirected, simple and finite, is the graph obtained by replacing each vertex $i$ of $H$ by $G_i$ and adding to the edges of all graphs in $\mathcal{G}$ the edges of the join $G_i \vee G_j$, for every edge $ij$ of $H$. Some well known graph operations are particular cases of the $H$-join of a family of graphs $\mathcal{G}$ as it is the case of the lexicographic product (also called composition) of two graphs $H$ and $G$, $H[G]$. During long time the known expressions for the determination of the entire spectrum of the $H$-join in terms of the spectra of its components and an associated matrix were limited to families of regular graphs.