On Even and Harmonic-Even Partial Cubes
نویسندگان
چکیده
Fukuda and Handa [7] asked whether every even partial cube G is harmonic-even. It is shown that the answer is positive if the isometric dimension of G equals its diameter which is in turn true for partial cubes with isometric dimension at most 6. Under an additional technical condition it is proved that an even partial cube G is harmonic-even or has two adjacent vertices whose diametrical vertices are at distance at least 4. Some related open problems are posed.
منابع مشابه
On even partial cubes
Fukuda and Handa [5] asked whether every even partial cube G is harmonic. It is shown that the answer is positive if the isometric dimension of G equals its diameter. This is in particular true if G has isometric dimension at most 6. Under an additional technical condition it is proved that an even G is harmonic or has two adjacent vertices whose diametrical vertices are at distance at least 4....
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ورودعنوان ژورنال:
- Ars Comb.
دوره 93 شماره
صفحات -
تاریخ انتشار 2009