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A Comprehensive Introduction to the Theory of Word-Representable Graphs. (arXiv:1705.05924v1 [math.CO])
来源于:arXiv
Letters $x$ and $y$ alternate in a word $w$ if after deleting in $w$ all
letters but the copies of $x$ and $y$ we either obtain a word $xyxy\cdots$ (of
even or odd length) or a word $yxyx\cdots$ (of even or odd length). A graph
$G=(V,E)$ is word-representable if and only if there exists a word $w$ over the
alphabet $V$ such that letters $x$ and $y$ alternate in $w$ if and only if
$xy\in E$.
Word-representable graphs generalize several important classes of graphs such
as circle graphs, $3$-colorable graphs and comparability graphs. This paper
offers a comprehensive introduction to the theory of word-representable graphs
including the most recent developments in the area. 查看全文>>