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François Jaeger conjectured in 1974 that every cyclically 4-connected cubic graph $G$ is dual hamiltonian, that is to say the vertices of $G$ can be partitioned into two subsets such that each subset induces a tree in $G$ . We shall make several remarks on this conjecture.

Some remarks on Menger's theorem

Bohdan Zelinka (1971)

Časopis pro pěstování matematiky

Some remarks on Ramsey matroids

Nešetřil, Jaroslav, Poljak, Svatopluk, Turzík, Daniel (1984)

Proceedings of the 11th Winter School on Abstract Analysis

Some remarks on the complement of a line graph

Dragoš M. Cvetković, Slobodan K. Simić (1974)

Publications de l'Institut Mathématique

Some remarks on the enumeration of rooted trees

Z. A. Łomnicki (1973)

Applicationes Mathematicae

Some remarks on the solutions of the equality per $(z I - A) = 0$ . (Einige Bemerkungen über die Lösungen der Gleichung per $(z I - A) = 0$ .)

Kräuter, Arnold Richard (1987)

Séminaire Lotharingien de Combinatoire [electronic only]

Some Remarks On The Structure Of Strong K-Transitive Digraphs

César Hernández-Cruz, Juan José Montellano-Ballesteros (2014)

Discussiones Mathematicae Graph Theory

A digraph D is k-transitive if the existence of a directed path (v0, v1, . . . , vk), of length k implies that (v0, vk) ∈ A(D). Clearly, a 2-transitive digraph is a transitive digraph in the usual sense. Transitive digraphs have been characterized as compositions of complete digraphs on an acyclic transitive digraph. Also, strong 3 and 4-transitive digraphs have been characterized. In this work we analyze the structure of strong k-transitive digraphs having a cycle of length at least k. We show...

Some remarks on α-domination

Franz Dahme, Dieter Rautenbach, Lutz Volkmann (2004)

Discussiones Mathematicae Graph Theory

Let α ∈ (0,1) and let $G = (V_{G}, E_{G}$ ) be a graph. According to Dunbar, Hoffman, Laskar and Markus [3] a set $D \subseteq V_{G}$ is called an α-dominating set of G, if $| N_{G} (u) \cap D | \geq α d_{G} (u)$ for all $u \in V_{G} ∖ D$ . We prove a series of upper bounds on the α-domination number of a graph G defined as the minimum cardinality of an α-dominating set of G.

Some results concerning reconstruction conjecture

Nýdl, Václav (1984)

Proceedings of the 12th Winter School on Abstract Analysis

Some results concerning the ends of minimal cuts of simple graphs

Xiaofeng Jia (2000)

Discussiones Mathematicae Graph Theory

Let S be a cut of a simple connected graph G. If S has no proper subset that is a cut, we say S is a minimal cut of G. To a minimal cut S, a connected component of G-S is called a fragment. And a fragment with no proper subset that is a fragment is called an end. In the paper ends are characterized and it is proved that to a connected graph G = (V,E), the number of its ends Σ ≤ |V(G)|.

Some Results on 4-Transitive Digraphs

Patricio Ricardo García-Vázquez, César Hernández-Cruz (2017)

Discussiones Mathematicae Graph Theory

Let D be a digraph with set of vertices V and set of arcs A. We say that D is k-transitive if for every pair of vertices u, v ∈ V, the existence of a uv-path of length k in D implies that (u, v) ∈ A. A 2-transitive digraph is a transitive digraph in the usual sense. A subset N of V is k-independent if for every pair of vertices u, v ∈ N, we have d(u, v), d(v, u) ≥ k; it is l-absorbent if for every u ∈ V N there exists v ∈ N such that d(u, v) ≤ l. A k-kernel of D is a k-independent and (k − 1)-absorbent...

Some results on chromatic polynomials of hypergraphs.

Walter, Manfred (2009)

The Electronic Journal of Combinatorics [electronic only]

Some results on graphs with at most two positive eigenvalues.

Petrović, Miroslav (1991)

Publications de l'Institut Mathématique. Nouvelle Série

Some results on metric trees

Asuman Güven Aksoy, Timur Oikhberg (2010)

Banach Center Publications

Using isometric embedding of metric trees into Banach spaces, this paper will investigate barycenters, type and cotype, and various measures of compactness of metric trees. A metric tree (T, d) is a metric space such that between any two of its points there is a unique arc that is isometric to an interval in ℝ. We begin our investigation by examining isometric embeddings of metric trees into Banach spaces. We then investigate the possible images x₀ = π((x₁ + ... + xₙ)/n), where π is a contractive...

Some results on semi-total signed graphs

Deepa Sinha, Pravin Garg (2011)

Discussiones Mathematicae Graph Theory

A signed graph (or sigraph in short) is an ordered pair $S = (S^{u}, σ)$ , where $S^{u}$ is a graph G = (V,E), called the underlying graph of S and σ:E → +, - is a function from the edge set E of $S^{u}$ into the set +,-, called the signature of S. The ×-line sigraph of S denoted by $L_{\times} (S)$ is a sigraph defined on the line graph $L (S^{u})$ of the graph $S^{u}$ by assigning to each edge ef of $L (S^{u})$ , the product of signs of the adjacent edges e and f in S. In this paper, first we define semi-total line sigraph and semi-total point sigraph of a given...

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