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 ...

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.

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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.

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

Advances on the hamiltonian problem: A survey, Graphs and Combinatorics, 19(2003). [pdf] Free Advertising! From Dover Books on Mathematics, 2012 Reprinting of: From CRC Press: Winner of American Library Association Choice Award - Outstanding Academic Titles, 2010.

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 ...

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 …

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…

The journal began publication in 1990. Since 2005, three volumes have been published annually. The journal is now electronic only, with immediate online access, free for both authors and readers. All content is freely available without charge to the user or their institution.

A Dynamic H-graph is just an animated directional H-graph. To put it another way, it is an H-graph where each item has an associated (directed) velocity as well as a position.

June 2, 2017 - Biró, Hujter, and Tuza introduced the concept of $H$-graphs (1992), intersection graphs of connected subgraphs of a subdivision of a graph $H$. They naturally generalize many important classes of graphs, e.g., interval graphs and circular-arc ...

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.

March 11, 2020 - Algorithmica - For a graph H, a graph G is an H-graph if it is an intersection graph of connected subgraphs of some subdivision of H. H-graphs naturally generalize several important graph classes...

Which is injective function. Hence H-graph is perfect square sum labeling.

May 27, 2021 - At the third post-Minkowskian order a two-loop double box graph, known as H-graph contributes. We consider the case where the two objects making up the binary system have equal masses.

In 1992 Biró, Hujter and Tuza introduced, for every fixed connected graph H, the class of H-graphs, defined as the intersection graphs of connected su...

March 26, 2021 - An L(h, k)-labeling of a graph G = (V, E) is a function f : V⟶[0, ∞) such that the positive difference between labels of the neighbouring vertices is at least h and the positive difference between ...

deleting at most one vertex we obtain an edgeless graph. Clearly, the (A0)-colouring number is the usual chromatic number and the · (A1)-colouring number is the clique cover number. The classes A0, A1, B1, ... Figure 1: A depiction of the eight classes for colouring numbers. For our purposes, we are interested in three families composed from the ... We consider the three associated F-colouring numbers. For convenience, we · denote τFi(H) by τi(H).