Related papers: Algebraic shifting of finite graphs

Applications of graph colouring often involve taking restrictions into account, and it is desirable to have multiple (disjoint) solutions. In the optimal case, where there is a partition into disjoint colourings, we speak of a packing.…

Let $G$ be a graph and $\mathcal {S}$ be a subset of $Z$. A vertex-coloring $\mathcal {S}$-edge-weighting of $G$ is an assignment of weight $s$ by the elements of $\mathcal {S}$ to each edge of $G$ so that adjacent vertices have different…

The aim of this paper is to show that any finite undirected bipartite graph can be considered as a polynomial $p \in \mathbb{N}[x]$, and any directed finite bipartite graph can be considered as a polynomial $p\in\mathbb{N}[x,y]$, and vise…

Bipartite graphs are a fundamental concept in graph theory with diverse applications. A graph is bipartite iff it contains no odd cycles, a characteristic that has many implications in diverse fields ranging from matching problems to the…

Let k be an integer and k \geq 3. A graph G is k-chordal if G does not have an induced cycle of length greater than k. From the definition it is clear that 3-chordal graphs are precisely the class of chordal graphs. Duchet proved that, for…

A bipartite graph is {\em pseudo 2--factor isomorphic} if all its 2--factors have the same parity of number of circuits. In \cite{ADJLS} we proved that the only essentially 4--edge-connected pseudo 2--factor isomorphic cubic bipartite graph…

The main contribution of this paper is a formula for the number of acyclic orientations of a complete bipartite, $K_{n_1,n_2},$ revealing that it is equal to the poly-Bernoulli number $B_{n_1}^{(-n_2)}$ introduced in 1997 by Kaneko. We also…

An important property of chordal graphs is that these graphs are characterized by existence of perfect elimination orderings on their vertex sets. In this paper, we generalize the notion of perfect elimination orderings to signed graphs,…

For integer $k\geq2$ and prime power $q$, the algebraic bipartite graph $D(k,q)$ proposed by Lazebnik and Ustimenko (1995) is meaningful not only in extremal graph theory but also in coding theory and cryptography. This graph is…

A $k$-graph $\mathcal{G}$ is asymmetric if there does not exist an automorphism on $\mathcal{G}$ other than the identity, and $\mathcal{G}$ is called minimal asymmetric if it is asymmetric but every non-trivial induced sub-hypergraph of…

When $\mathcal{C}$ is a chordal clutter in the sense of Woodroofe or Emtander, we show that the complement clutter is edgewise strongly shellable. When $\mathcal{C}$ is indeed a finite simple graph, we study various characterizations of…

Let $k$ be a positive integer and let $G$ be a graph with vertex set $V(G)$. A subset $D \subseteq V(G)$ is a $k$-dominating set if every vertex outside $D$ is adjacent to at least $k$ vertices in $D$. The $k$-domination number…

An antimagic labeling of a directed graph $D$ with $n$ vertices and $m$ arcs is a bijection from the set of arcs of $D$ to the integers $\{1, \cdots, m\}$ such that all $n$ oriented vertex sums are pairwise distinct, where an oriented…

Let $\Gamma$ be a $G$-symmetric graph with vertex set $V$. We suppose that $V$ admits a $G$-partition $\mathcal{B} = \{ B_0, ... , B_b \}$, with parts of size $v$, and that the quotient graph induced on $\mathcal B$ is a complete graph of…

A subgraph $G'$ of a graph $G$ is nice if $G-V(G')$ has a perfect matching. Nice subgraphs play a vital role in the theory of ear decomposition and matching minors of matching covered graphs. A vertex $u$ of a cubic graph is nice if $u$ and…

A graph $G$ is equimatchable if any matching in $G$ is a subset of a maximum-size matching. It is known that any $2$-connected equimatchable graph is either bipartite or factor-critical. We prove that for any vertex $v$ of a $2$-connected…

In this article we study higher homological properties of $n$-levelled algebras and connect them to properties of the underlying graphs. Notably, to each $2$-representation-finite quadratic monomial algebra $\Lambda$ we associate a…

Recently, Alon, Cambie, and Kang introduced asymmetric list coloring of bipartite graphs, where the size of each vertex's list depends on its part. For complete bipartite graphs, we fix the list sizes of one part and consider the resulting…

A bipartite graph $G=(V,E)$ with $V=V_1\cup V_2$ is biregular if all the vertices of a stable set $V_i$ have the same degree $r_i$ for $i=1,2$. In this paper, we give an improved new Moore bound for an infinite family of such graphs with…

The difference between the two largest eigenvalues of the adjacency matrix of a graph $G$ is called the spectral gap of $G.$ If $G$ is a regular graph, then its spectral gap is equal to algebraic connectivity. Abdi, Ghorbani and Imrich, in…