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

AKCE 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 Chromatic Number of Sparse Random Graphs

Random 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
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Anti-Ramsey number of intersecting cliques

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
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Tight Approximation and Kernelization Bounds for Vertex-Disjoint Shortest Paths. [PDF]

Theory Comput Syst
Bentert M, Fomin FV, Golovach PA.
europepmc +1 more source

Homophily within and across groups. [PDF]