We propose an object clique potential for semantic segmentation. Our object clique potential addresses the misclassified object-part issues arising in solutions based on fully-convolutional networks. Our object clique set, compared to that yielded from segment-proposal-based approaches, is with a significantly smaller size, making our method consume notably less computation. Regarding system de...

Given a linear order < on the vertices of a graph, an obstruction is an induced P4 abcd such that a < b and d < c. A linear order without any obstruction is called perfect. A graph is perfectly orderable if its vertex set has some perfect order. In the graph G, for two vertices x and y, x clique-dominates y if every maximum size clique containing y, contains x too. We prove the following result...

We show that Edge Dominating Set, Hamiltonian Cycle, and Graph Coloring are W [1]-hard parameterized by clique-width. It was an open problem, explicitly mentioned in several papers, whether any of these problems is fixed parameter tractable when parameterized by the clique-width, that is, solvable in time g(k) · nO(1) on n-vertex graphs of clique-width k, where g is some function of k only. Our...

An m-clique hole is a sequence φ = (Φ1,Φ2, . . . ,Φm) of m distinct cliques such that |Φi| ≤ m for all i = 1, 2, . . . ,m, and whose clique graph is a hole on m vertices. That is, φ is an m-clique hole if for all i 6= j, i, j = 1, 2, . . . ,m, Φi∩Φj 6= ∅ if and only if (j − 1) mod m = (j + 1) mod m = i mod m. This paper derives a sufficient and necessary condition on m-colorability of m-clique ...

Similar to the tree-width (twd), the clique-width (cwd) is an invariant of graphs. A well known relationship between tree-width and clique-width is that cwd(G) ≤ 3 · 2. It is also known that treewidth of Cactus graphs is 2, therefore the clique-width for those graphs is smaller or equal than 6. In this paper, it is shown that the clique-width of Cactus graphs is smaller or equal to 4 and we pre...

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. We describe characterizations relative to edge clique graphs and some classes of chordal graphs, such as starlike, starlike-threshold, split and threshold graphs. In particular, a known necessary condition for a graph to be an edge c...

In this paper we consider a branch-and-bound algorithm for the maximum clique problem. We introduce cost based filtering techniques for the so-called candidate set (i.e. a set of nodes that can possibly extend the clique in the current choice point). Doing this, we can reduce the number of choice points visited by a typical factor of 10 – 50. Additionally, we present a taxonomy of upper bounds ...

We show that edge-clique graphs of cocktail party graphs have unbounded rankwidth. This, and other observations lead us to conjecture that the edge-clique cover problem is NP-complete for cographs. We show that the independent set problem on edge-clique graphs of cographs and of distance-hereditary graphs can be solved in polynomial time. We show that the independent set problem on edge-clique ...

We define an approach to identify overlapping communities in multiplex networks, extending the popular clique percolation method for simple graphs. The extension requires to rethink the basic concepts on which the clique percolation algorithm is based, including cliques and clique adjacency, to allow the presence of multiple types of edges.

The clique vector c(G) of a graph G is the sequence (c1, c2, . . . , cd) in N, where ci is the number of cliques in G with i vertices and d is the largest cardinality of a clique in G. In this note, we use tools from commutative algebra to characterize all possible clique vectors of k-connected chordal graphs.