A clique-transversal of a graph G is a subset of vertices that meets all the cliques of G. A clique-independent set is a collection of pairwise vertex-disjoint cliques. The clique-transversal number and clique-independence number of G are the sizes of a minimum clique-transversal and a maximum clique-independent set of G, respectively. A graph G is clique-perfect if the sizes of a minimum cliqu...

In this paper, two notions, the clique irreducibility and clique vertex irreducibility are discussed. A graph G is clique irreducible if every clique in G of size at least two, has an edge which does not lie in any other clique of G and it is clique vertex irreducible if every clique in G has a vertex which does not lie in any other clique of G. It is proved that L(G) is clique irreducible if a...

The clique graph K(G) of a graph G is the intersection graph of all its (maximal) cliques, and G is said to be clique divergent if the order of its n-th iterated clique graph Kn(G) tends to infinity with n. In general, deciding whether a graph is clique divergent is not known to be computable. We characterize the dynamical behavior under the clique operator of circulant graphs of the form Cn(a,...

Motivated by an application in condensed matter physics and quantum information theory, we prove that every non-null even-hole-free claw-free graph has a simplicial clique, is, clique $K$ such for vertex $v \in K$, the set of neighbours $v$ outside is clique. In fact, existence more general class graphs defined forbidden induced subgraphs.

Seese’s conjecture for finite graphs states that monadic second-order logic (MSO) is undecidable on all graph classes of unbounded clique-width. We show to establish this it would suffice grids size can be interpreted in two families classes: minimal hereditary clique-width; and antichains clique-width under the induced subgraph relation. explore currently known former category indeed them.

We approximately solve, by reduction to Maximum Clique, the graph k-coloring NP-hard problem in a binary weights Hoppeld net special case. This network was used earlier to approximately solve Maximum Clique and some other NP-hard problems by reduction to Maximum Clique. We determine k-coloring approximation performance on random graphs and on one other distribution of \harder" graphs. We compar...