… graph whose largest clique has size at most three is a clique graph. In Section 3 we show
an edge-clique graph that is not a clique graph and prove that it is a minimum counterexample …

… , and that if G is either an interval graph or a line graph, then so too is K(G). An algorithm is
… whether a graph is an edge-clique graph. A new graph called the STP graph is introduced …

… edges of a graph. In this paper, we present a variety of results on edge clique coverings, and
… We are writing this paper at this time because edge clique coverings seem to have a wide …

… Cover (ECC) problem, given an undirected graph G and an integer k, we ask whether one
can choose k cliques in G such that each edge of G is contained in at least one of the chosen …

… which are the graphs whose edge clique graphs belong to C. Finally, … graphs of a given
class are edge clique graphs. We solve this problem for both starlike-threshold and split graphs…

… EDGE-CLIQUE: The vertices of G correspond to the edges of some graph H, with two
vertices adjacent in G whenever their corresponding edges in H belong to a same clique. …

… for l-coloring the edge-clique graph of a threshold graph is provided. Moreover, we characterize
edge-clique graphs of outerplanar graphs as particular outerplanar graphs, so the same …

… Note that G ′ is a ( 0 , 2 ) -graph with n + N vertices, where N is the number of edges of an
… an edge clique partition Ω of G of size at most q if and only if there is an edge clique partition …

… The edge clique graph of a graph G is one having as vertices the edges of G, two vertices
being adjacent if the corresponding edges of G belong to a common clique. … A necessary …

… An edge clique cover of a graph G is a set of cliques Q = { Q 1 , … , Q t } that covers the edges
… The edge clique cover number θ ( G ) is the minimum number of cliques in an edge clique …