A perfect graph is critical if the deletion of any edge results in an imperfect graph. We give examples of such graphs and prove some basic properties. We relate critically perfect graphs to well-known classes of perfect graphs, investigate the structure of the class of critically perfect graphs, and study operations preserving critical perfectness.

let $g$ be a simple graph of order $n$ and size $m$.the edge covering of $g$ is a set of edges such that every vertex of $g$ is incident to at least one edge of the set. the edge cover polynomial of $g$ is the polynomial$e(g,x)=sum_{i=rho(g)}^{m} e(g,i) x^{i}$,where $e(g,i)$ is the number of edge coverings of $g$ of size $i$, and$rho(g)$ is the edge covering number of $g$. in this paper we stud...

let g=(v,e) be a simple graph. an edge labeling f:e to {0,1} induces a vertex labeling f^+:v to z_2 defined by $f^+(v)equiv sumlimits_{uvin e} f(uv)pmod{2}$ for each $v in v$, where z_2={0,1} is the additive group of order 2. for $iin{0,1}$, let e_f(i)=|f^{-1}(i)| and v_f(i)=|(f^+)^{-1}(i)|. a labeling f is called edge-friendly if $|e_f(1)-e_f(0)|le 1$. i_f(g)=v_f(1)-v_f(0) is called the edge-f...

The Balanced Subgraph problem (edge deletion variant) asks for a 2-coloring of a graph that minimizes the inconsistencies with given edge labels. It has applications in social networks, systems biology, and integrated circuit design. We present an exact algorithm for Balanced Subgraph based on a combination of data reduction rules and a fixed-parameter algorithm. The data reduction is based on ...

This thesis is concerned with how grammar determines the phonological consequence of syntactic dislocation. It centers on a hypothesis regarding the linearization of movement chains the Edge Condition on Copy Deletion, eventually named the Edge Condition in the last chapter, when it receives its final formulation. The empirical phenomena under investigation include (i) predicate cleft construct...

We present several classes of facet-deening inequalities to strengthen polyhedra arising as subsystems of network design problems with survivability constraints. These problems typically involve assigning capacities to a network with multicommodity demands, such that after a vertex-or edge-deletion at least some prescribed fraction of each demand can be routed.

We show, in a unified manner, that there exist linear time algorithms for many combinatorial problems defined on the class of series-parallel graphs. These include (i) the decision problem, and (ii) the minimum edge (vertex) deletion problem both with respect to a property characterized by a finite number of forbidden graphs, and (iii) the generalized matching problem.

We study the complexity of turning a given graph, by edge editing, into a target graph whose critical-clique graph is any fixed graph. The problem came up in practice, in an effort of mining huge word similarity graphs for well structured word clusters. It also adds to the rich field of graph modification problems. We show in a generic way that several variants of this problem are in SUBEPT. As...

The problem of efficiently maintaining attributes of a dynamic forest modified by edge insertions and deletions is one that has been extensively studied. In this paper, we present a novel dynamic data structure that supports edge insertions and deletions while maintaining non-local properties in O(log n) time. We use this data structure to solve an important open problem: a dynamic data structu...