Degree-equipartite graphs

Details Degree-equipartite graphs Degree-equipartite graphs

2011-08-08

arxiv.org/abs/1108.1606v1

Discrete Math., 311 (2011) 888--891

Mathematics

Combinatorics

6 pages

Scientific paper

10.1016/j.disc.2011.02.018

A graph $G$ of order $2n$ is called degree-equipartite if for every $n$-element set $A\subseteq V(G)$, the degree sequences of the induced subgraphs $G[A]$ and $G[V(G)\setminus A]$ are the same. In this paper, we characterize all degree-equipartite graphs. This answers Problem 1 in the paper by Gr\"{u}nbaum et al [B. Gr\"{u}nbaum, T. Kaiser, D. Kr\'{a}l, and M. Rosenfeld, Equipartite graphs, {\it Israel J. Math.} {\bf 168} (2008), 431-444].

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