@inbook {IOPORT.05825875,
    author       = {Marchant, Edward and Thomason, Andrew},
    title        = {Extremal graphs and multigraphs with two weighted colours.},
    year         = {2010},
    booktitle    = {Fete of combinatorics and computer science. Selected papers of the conference held in Keszthely, Hungary, August 11--15, 2008 dedicated to L\'aszl\'o Lov\'asz on the occasion of his 60th birthday},
    isbn         = {978-3-642-13579-8},
    pages        = {239-286},
    publisher    = {Dordrecht: Springer; Budapest: J\'anos Bolyai Mathematical Society},
    abstract     = {A $2$-colored multigraph $G$ is a multigraph whose edge set is the union of two simple graphs $G_{r}$ and $G_{b}$ on the same vertex set $V(G)$. The underlying graph $G_{u}$ of $G$ is a simple graph with vertex set $V(G)$, two vertices are adjacent in $G_{u}$ if they are adjacent in at least one of $G_{r}$ and $G_{b}$. The classical extremal graph problem concerning the maximum number of edges in graphs on $n$ vertices that do not contain the graph $H$ as a subgraph is the Turan-type extremal problem. The extremal problem considered in this work is the following: Let $1\leq p\leq 1$ and $ q=1-p$. For a fixed $H$, find the maximum weight $p|E(G_{r})|+q|E(G_{b})|$ for large colored multigraphs $G$ that do not contain $H$ as a subgraph. Motivated by applications, the author considered the maximum restricted to those $G$ whose underlying graph is complete. They describe some basic features of the extremal function in general and some specific examples are studied in detail.},
    reviewer     = {Mohammed M. M. Jaradat},
    identifier   = {05825875},
}