相关论文: On the Structure of the Minimum Critical Independe…

Let $G$ be a simple graph with vertex set $V\left( G\right) $. A set $S\subseteq V\left( G\right) $ is independent if no two vertices from $S$ are adjacent, and by $\mathrm{Ind}(G)$ we mean the family of all independent sets of $G$. The…

Let G be a simple graph with vertex set V(G). A subset S of V(G) is independent if no two vertices from S are adjacent. By Ind(G) we mean the family of all independent sets of G while core(G) and corona(G) denote the intersection and the…

Let G=(V,E) be a graph. A set S is independent if no two vertices from S are adjacent, alpha(G) is the size of a maximum independent set, and core(G) is the intersection of all maximum independent sets. The number d(X)=|X|-|N(X)| is the…

Let G=(V,E) be a graph. A set S is independent if no two vertices from S are adjacent. The independence number alpha(G) is the cardinality of a maximum independent set, and mu(G) is the size of a maximum matching. The number…

Let $G$ be a simple graph with vertex set $V(G)$. A set $S\subseteq V(G)$ is independent if no two vertices from $S$ are adjacent. For $X\subseteq V(G)$, the difference of $X$ is $d(X) = |X|-|N(X)|$ and an independent set $A$ is critical if…

Let $G$ be a finite simple graph. For $X \subset V(G)$, the difference of $X$, $d(X) := |X| - |N (X)|$ where $N(X)$ is the neighborhood of $X$ and $\max \, \{d(X):X\subset V(G)\}$ is called the critical difference of $G$. $X$ is called a…

A set S is independent in a graph G if no two vertices from S are adjacent. The independence number alpha(G) is the cardinality of a maximum independent set, while mu(G) is the size of a maximum matching in G. If alpha(G)+mu(G)=|V|, then…

Let $G$ be a finite simple graph. An independent set $I$ of $G$ is critical if $\left|I\right|-\left|N(I)\right|\ge\left|J\right|-\left|N(J)\right|$ for every independent set $J$ of $G$. A critical independent set is maximum if it has…

A set $S\subseteq V$ is \textit{independent} in a graph $G=\left( V,E\right) $ if no two vertices from $S$ are adjacent. The \textit{independence number} $\alpha(G)$ is the cardinality of a maximum independent set, while $\mu(G)$ is the…

A set S is independent in a graph G if no two vertices from S are adjacent. By core(G) we mean the intersection of all maximum independent sets. The independence number alpha(G) is the cardinality of a maximum independent set, while mu(G)…

Let alpha(G) be the cardinality of a independence set of maximum size in the graph G, while mu(G) is the size of a maximum matching. G is a Konig--Egervary graph if its order equals alpha(G) + mu(G). The set core(G) is the intersection of…

Let $\alpha(G)$ denote the cardinality of a maximum independent set, while $\mu(G)$ be the size of a maximum matching in $G=\left( V,E\right) $. Let $\xi(G)$ denote the size of the intersection of all maximum independent sets. It is known…

Let $G=(V,E)$ be a simple graph. A set $I\subseteq V$ is an independent set, if no two of its members are adjacent in $G$. The $k$-independent graph of $G$, $I_k (G)$, is defined to be the graph whose vertices correspond to the independent…

A set $S\subseteq V(G)$ is independent (or stable) if no two vertices from $S$ are adjacent, and by $\mathrm{Ind}(G)$ we mean the set of all independent sets of $G$. A set $A\in\mathrm{Ind}(G)$ is critical (and we write $A\in CritIndep(G)$)…

The independence number $\alpha(G)$ is the cardinality of a maximum independent set, while $\mu(G)$ is the size of a maximum matching in $G$. If $\alpha(G)+\mu(G)$ equals the order of $G$, then $G$ is called a Konig-Egervary graph. The…

Let G be a simple graph with vertex set V(G). A set S is independent if no two vertices from S are adjacent. The graph G is known to be a Konig-Egervary if alpha(G)+mu(G)= |V(G)|, where alpha(G) denotes the size of a maximum independent set…

The independent domination number $i(G)$ of a graph $G$ is the minimum cardinality of a maximal independent set of $G$, also called an $i(G)$-set. The $i$-graph of $G$, denoted $\mathcal{I}(G)$, is the graph whose vertices correspond to the…

An independent set $I_c$ is a \textit{critical independent set} if $|I_c| - |N(I_c)| \geq |J| - |N(J)|$, for any independent set $J$. The \textit{critical independence number} of a graph is the cardinality of a maximum critical independent…

Let $G$ be a graph with vertex set $V(G)$ and edge set $E(G)$. A set $I_0(G) \subseteq V(G)$ is a vertex independent set if no two vertices in $I_0(G)$ are adjacent in $G$. We study $\alpha_1(G)$, which is the maximum cardinality of a set…

For a graph G and integer r \geq 1 we denote the family of independent r-sets of V(G) by I^{(r)}(G). A graph G is said to be r-EKR if no intersecting subfamily of I^{(r)}(G) is larger than the largest such family all of whose members…