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We give an $O(n^4)$ algorithm to find a minimum clique cover of a (bull, $C_4$)-free graph, or equivalently, a minimum colouring of a (bull, $2K_2$)-free graph, where $n$ is the number of vertices of the graphs.
Multiple interval graphs are variants of interval graphs where instead of a single interval, each vertex is assigned a set of intervals on the real line. We study the complexity of the MAXIMUM CLIQUE problem in several classes of multiple interval gr
An $(m, n)$-colored mixed graph is a graph having arcs of $m$ different colors and edges of $n$ different colors. A graph homomorphism of an $(m, n$)-colored mixed graph $G$ to an $(m, n)$-colored mixed graph $H$ is a vertex mapping such that if $uv$
Threshold graphs are a class of graphs that have many equivalent definitions and have applications in integer programming and set packing problems. A graph is said to have a threshold cover of size $k$ if its edges can be covered using $k$ threshold
For which graphs $F$ is there a sparse $F$-counting lemma in $C_4$-free graphs? We are interested in identifying graphs $F$ with the property that, roughly speaking, if $G$ is an $n$-vertex $C_4$-free graph with on the order of $n^{3/2}$ edges, then
A hole is a chordless cycle with at least four vertices. A pan is a graph which consists of a hole and a single vertex with precisely one neighbor on the hole. An even hole is a hole with an even number of vertices. We prove that a (pan, even hole)-f