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Complexity Results on Graphs with Few Cliques

open access: yesDiscrete Mathematics & Theoretical Computer Science, 2007
A graph class has few cliques if there is a polynomial bound on the number of maximal cliques contained in any member of the class. This restriction is equivalent to the requirement that any graph in the class has a polynomial sized intersection ...
Bill Rosgen, Lorna Stewart
doaj  

Integral sum graphs Gn and G-r,n are perfect graphs

open access: yesAKCE International Journal of Graphs and Combinatorics
A graph G is an integral sum graph (sum graph) if its vertices can be labeled with distinct integers (positive integers) so that e = uv is an edge of G if and only if the sum of the labels on vertices u and v is also a label in G. A graph G is perfect if
Julia K. Abraham   +4 more
doaj   +1 more source

The Clique-Width of Minimal Series-Parallel Digraphs

open access: yesAlgorithms
MSP DAGs (short for minimal series-parallel digraphs) can be defined from the single vertex graph by applying the parallel composition and series composition.
Frank Gurski, Ruzayn Quaddoura
doaj   +1 more source

The Clique Chromatic Number of Sparse Random Graphs

open access: yesRandom Structures & Algorithms
ABSTRACT The clique chromatic number of a graph is the smallest number of colors in a vertex coloring so that no maximal clique is monochromatic. In this paper, we determine the order of magnitude of the clique chromatic number of the random graph  for most edge‐probabilities  in the range .
Manuel Fernandez, Lutz Warnke
openaire   +2 more sources

Anti-Ramsey number of intersecting cliques

open access: yes
An edge-colored graph is called a rainbow graph if all its edges have distinct colors. The anti-Ramsey number $ar(n, G)$, for a graph $G$ and a positive integer $n$, is defined as the minimum number of colors $r$ such that every exact $r$-edge-coloring of the complete graph $K_n$ contains at least one rainbow copy of $G$. A $(k, r)$-fan graph, denoted $
Lu, Hongliang, Luo, Xinyue, Ma, Xinxin
openaire   +2 more sources

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