# A Combinatorial Theorem on Ordered Circular Sequences of n 1 u's and n 2 v' s with Application to Kernel-perfect Graphs

A Combinatorial Theorem on Ordered Circular Sequences of n 1 u's and n 2 v' s with Application to... An ordered circular permutation S of u's and v' s is called an ordered circular sequence of u' s and v' s. A kernel of a digraph G=(V,A) is an independent subset of V, say K, such that for any vertex v i in V\K there is an arc from v i to a vertex v j in K. G is said to be kernel-perfect (KP) if every induced subgraph of G has a kernel. G is said to be kernel-perfect-critical (KPC) if G has no kernel but every proper induced subgraph of G has a kernel. The digraph $$G = {\left( {V,A} \right)} = \ifmmode\expandafter\vec\else\expandafter\vecabove\fi{C}_{n} {\left( {j_{1} ,j_{2} , \cdots ,j_{k} } \right)}$$ is defined by: V(G)={0,1,...,n−1}, A(G)={uv | v−u≡j, (mod n) for 1 ≤i≤k}. http://www.deepdyve.com/assets/images/DeepDyve-Logo-lg.png Acta Mathematicae Applicatae Sinica Springer Journals

# A Combinatorial Theorem on Ordered Circular Sequences of n 1 u's and n 2 v' s with Application to Kernel-perfect Graphs

, Volume 19 (1) – Jan 1, 2003
6 pages

/lp/springer-journals/a-combinatorial-theorem-on-ordered-circular-sequences-of-n-1-u-s-and-n-V3HeoAKXHR
Publisher
Springer Journals
Subject
Mathematics; Applications of Mathematics; Math Applications in Computer Science; Theoretical, Mathematical and Computational Physics
ISSN
0168-9673
eISSN
1618-3932
DOI
10.1007/s10255-003-0079-1
Publisher site
See Article on Publisher Site

### Abstract

An ordered circular permutation S of u's and v' s is called an ordered circular sequence of u' s and v' s. A kernel of a digraph G=(V,A) is an independent subset of V, say K, such that for any vertex v i in V\K there is an arc from v i to a vertex v j in K. G is said to be kernel-perfect (KP) if every induced subgraph of G has a kernel. G is said to be kernel-perfect-critical (KPC) if G has no kernel but every proper induced subgraph of G has a kernel. The digraph $$G = {\left( {V,A} \right)} = \ifmmode\expandafter\vec\else\expandafter\vecabove\fi{C}_{n} {\left( {j_{1} ,j_{2} , \cdots ,j_{k} } \right)}$$ is defined by: V(G)={0,1,...,n−1}, A(G)={uv | v−u≡j, (mod n) for 1 ≤i≤k}.

### Journal

Acta Mathematicae Applicatae SinicaSpringer Journals

Published: Jan 1, 2003

### References

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