Related papers: Unmixed bipartite graphs
In this paper, we study oriented bipartite graphs. In particular, we introduce "bitransitive" graphs. Several characterizations of bitransitive bitournaments are obtained. We show that bitransitive bitounaments are equivalent to acyclic…
This work considers new entropy-based proofs of some known, or otherwise refined, combinatorial bounds for bipartite graphs. These include upper bounds on the number of the independent sets, lower bounds on the minimal number of colors in…
We give a full characterisation of the symmetries of unlabelled triangulations and derive a constructive decomposition of unlabelled triangulations depending on their symmetries. As an application of these results we can deduce a complete…
In this paper we consider the separability problem for bipartite quantum states arising from graphs. Earlier it was proved that the degree criterion is the graph-theoretic counterpart of the familiar positive partial transpose criterion for…
Bipartite Graph is often a realistic model of complex networks where two different sets of entities are involved and relationship exist only two entities belonging to two different sets. Examples include the user-item relationship of a…
In this note, we prove an interesting result about perfect matchings in a complete bipartite graph with 2n vertices on each side, whose edges are colored in red and blue such that each vertex is part of n red edges and n blue edges.
We give an elementary, self-contained, and purely combinatorial proof of the Rayleigh monotonicity property of graphs.
In this paper, firstly, we provide some necessary and sufficient conditions for generalized Cayley graphs on abelian groups to be bipartite. Secondly, we deduce several necessary and sufficient conditions for generalized Cayley graphs on…
We present a simple combinatorial model for quasipositive surfaces and positive braids, based on embedded bipartite graphs. As a first application, we extend the well-known duality on standard diagrams of torus links to twisted torus links.…
Let $G$ be a group and $L(G)$ be the set of all subgroups of $G$. We introduce a bipartite graph $\mathcal{B}(G)$ on $G$ whose vertex set is the union of two sets $G \times G$ and $L(G)$, and two vertices $(a, b) \in G \times G$ and $H \in…
In this paper we determine the exact values of the signed domination number, signed total domination number, and minus domination number of complete multipartite graphs, which substantially generalizes some previous results obtained for…
For each Boolean graph $B_n$, it is proved that both $B_n$ and its complement graph $\overline{B_n}$ are vertex decomposable. It is also proved that $B_n$ is an unmixed graph, thus it is also Cohen-Macaulay.
In enumerative combinatorics, it is often a goal to enumerate both labeled and unlabeled structures of a given type. The theory of combinatorial species is a novel toolset which provides a rigorous foundation for dealing with the…
This paper proposes an efficient method to construct the bipartite graph with as many edges as possible while without introducing the shortest cycles of length equal to 4. The binary matrix associated with the bipartite graph described…
This paper studies the structure of graphs with given tree-width and excluding a fixed complete bipartite subgraph, which generalises the bounded degree setting. We give a new structural description of such graphs in terms of so-called…
Global Markov properties in mixed graphs are usually formulated in terms of the path-oriented m-separation or by use of augmented graphs (similar to moral graphs in the case of directed acyclic graphs). We provide an alternative…
The existence of an on-line competitive algorithm for coloring bipartite graphs remains a tantalizing open problem. So far there are only partial positive results for bipartite graphs with certain small forbidden graphs as induced…
Mixed graphs can be seen as digraphs that have both arcs and edges (or digons, that is, two opposite arcs). In this paper, we consider the case where such graphs are bipartite. As main results, we show that in this context the Moore-like…
In this paper, we show that unswitchable graphs are a proper subclass of split graphs, and exploit this fact to propose efficient algorithms for their recognition and generation.
We give a complete characterization of mixed unit interval graphs, the intersection graphs of closed, open, and half-open unit intervals of the real line. This is a proper superclass of the well known unit interval graphs. Our result solves…