A characterization of graphs in which some minimum dominating set covers all the edges
A characterization of the decay number of a connected graph
A decomposition algorithm for the oriented adjacency graph of the triangulations of a bordered surface with marked points.
A Décomposition Theorem on Euclidean Steiner Minimal Trees.
A degree condition for the existence of -factors with prescribed properties.
A direct decomposition of 3-connected planar graphs.
A Finite Characterization and Recognition of Intersection Graphs of Hypergraphs with Rank at Most 3 and Multiplicity at Most 2 in the Class of Threshold Graphs
We characterize the class [...] L32 of intersection graphs of hypergraphs with rank at most 3 and multiplicity at most 2 by means of a finite list of forbidden induced subgraphs in the class of threshold graphs. We also give an O(n)-time algorithm for the recognition of graphs from [...] L32 in the class of threshold graphs, where n is the number of vertices of a tested graph.
A forbidden subgraphs characterization and a polynomial algorithm for randomly decomposable graphs
A generalization of Smith's theorem
A Havel-Hakimi type procedure and a sufficient condition for a sequence to be potentially -graphic
The split graph on vertices is denoted by . A non-increasing sequence of nonnegative integers is said to be potentially -graphic if there exists a realization of containing as a subgraph. In this paper, we obtain a Havel-Hakimi type procedure and a simple sufficient condition for to be potentially -graphic. They are extensions of two theorems due to A. R. Rao (The clique number of a graph with given degree sequence, Graph Theory, Proc. Symp., Calcutta 1976, ISI Lect. Notes Series...
A lower bound for the packing chromatic number of the Cartesian product of cycles
Let G = (V, E) be a simple graph of order n and i be an integer with i ≥ 1. The set X i ⊆ V(G) is called an i-packing if each two distinct vertices in X i are more than i apart. A packing colouring of G is a partition X = {X 1, X 2, …, X k} of V(G) such that each colour class X i is an i-packing. The minimum order k of a packing colouring is called the packing chromatic number of G, denoted by χρ(G). In this paper we show, using a theoretical proof, that if q = 4t, for some integer t ≥ 3, then 9...
A matching and a Hamiltonian cycle of the fourth power of a connected graph
The following result is proved: Let be a connected graph of order . Then for every matching in there exists a hamiltonian cycle of such that .
A Maximum Resonant Set of Polyomino Graphs
A polyomino graph P is a connected finite subgraph of the infinite plane grid such that each finite face is surrounded by a regular square of side length one and each edge belongs to at least one square. A dimer covering of P corresponds to a perfect matching. Different dimer coverings can interact via an alternating cycle (or square) with respect to them. A set of disjoint squares of P is a resonant set if P has a perfect matching M so that each one of those squares is M-alternating. In this paper,...
A Neighborhood Condition for Fractional ID-[A, B]-Factor-Critical Graphs
Let G be a graph of order n, and let a and b be two integers with 1 ≤ a ≤ b. Let h : E(G) → [0, 1] be a function. If a ≤ ∑e∋x h(e) ≤ b holds for any x ∈ V (G), then we call G[Fh] a fractional [a, b]-factor of G with indicator function h, where Fh = {e ∈ E(G) : h(e) > 0}. A graph G is fractional independent-set-deletable [a, b]-factor-critical (in short, fractional ID-[a, b]- factor-critical) if G − I has a fractional [a, b]-factor for every independent set I of G. In this paper, it is proved...
A Note on a Bermond's Conjecture
A Note On Analogies Between Characteristic And The Matching Polynomial Of A Graph
A note on careful packing of a graph
Let G be a simple graph of order n and size e(G). It is well known that if e(G) ≤ n-2, then there is an edge-disjoint placement of two copies of G into Kₙ. We prove that with the same condition on size of G we have actually (with few exceptions) a careful packing of G, that is an edge-disjoint placement of two copies of G into Kₙ∖Cₙ.
A note on cycle double covers in Cayley graphs.
A note on divisibility of the number of matchings of a family of graphs.
A note on domatically critical and cocritical graphs