There are no finite partial cubes of girth more than six and minimum degree at least three
نویسنده
چکیده
Partial cubes are graphs isometrically embeddable into hypercubes. We analyze how isometric cycles in partial cubes behave and derive that every partial cube of girth more than six must have vertices of degree less than three. As a direct corollary we get that every regular partial cube of girth more than six is an even cycle. Along the way we prove that every partial cube G with girth more than six is the so-called zone graph and therefore 2n(G) − m(G) − i(G) + ce(G) = 2 holds, where i(G) is the isometric dimension of G and ce(G) its convex excess.
منابع مشابه
There are no finite partial cubes of girth more than 6 and minimum degree at least 3
Partial cubes are graphs isometrically embeddable into hypercubes. We analyze how isometric cycles in partial cubes behave and derive that every partial cube of girth more than six must have vertices of degree less than three. As a direct corollary we get that every regular partial cube of girth more than six is an even cycle. Along the way we prove that every partial cube G with girth more tha...
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My research revolves around structural and extremal aspects of Graph Theory, particularly problems involving girth and distance, trees, cycles in graphs, and some variations of Ramsey theory. I have also done some work in generalized graph colorings and graph labellings. My other interests include graph decomposi-tions and packings, perfect graphs, matching theory, hypergraphs and coding theory...
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ورودعنوان ژورنال:
- CoRR
دوره abs/1503.04706 شماره
صفحات -
تاریخ انتشار 2015