The existence problem for colour critical linear hypergraphs

1978 ◽  
Vol 32 (3-4) ◽  
pp. 273-282 ◽  
Author(s):  
H. L. Abbott ◽  
A. C. Liu
1982 ◽  
Vol 3 (2) ◽  
pp. 159-172 ◽  
Author(s):  
Ranjan N. Naik ◽  
S.B. Rao ◽  
S.S. Shrikhande ◽  
N.M. Singhi

2011 ◽  
Vol 159 (1) ◽  
pp. 46-52 ◽  
Author(s):  
Moo Young Sohn ◽  
Dongseok Kim ◽  
Young Soo Kwon ◽  
Jaeun Lee

10.37236/2370 ◽  
2012 ◽  
Vol 19 (2) ◽  
Author(s):  
Ioan Tomescu
Keyword(s):  

Let $r\geq 1$ be an integer. An $h$-hypergraph $H$ is said to be $r$-quasi-linear (linear for $r=1$) if any two edges of $H$ intersect in 0 or $r$ vertices. In this paper it is shown that $r$-quasi-linear paths $P_{m}^{h,r}$ of length $m\geq 1$ and cycles $C_{m}^{h,r}$ of length $m\geq 3$ are chromatically unique in the set of $h$-uniform $r$-quasi-linear hypergraphs provided $r\geq 2$ and $h\geq 3r-1$. 


2013 ◽  
Vol 22 (6) ◽  
pp. 829-858 ◽  
Author(s):  
JILL DIZONA ◽  
BRENDAN NAGLE

For k-graphs F0 and H, an F0-packing of H is a family $\mathscr{F}$ of pairwise edge-disjoint copies of F0 in H. Let νF0(H) denote the maximum size |$\mathscr{F}$| of an F0-packing of H. Already in the case of graphs, computing νF0(H) is NP-hard for most fixed F0 (Dor and Tarsi [6]).In this paper, we consider the case when F0 is a fixed linear k-graph. We establish an algorithm which, for ζ > 0 and a given k-graph H, constructs in time polynomial in |V(H)| an F0-packing of H of size at least νF0(H) − ζ |V(H)|k. Our result extends one of Haxell and Rödl, who established the analogous algorithm for graphs.


Wave Motion ◽  
1994 ◽  
Vol 20 (3) ◽  
pp. 233-244 ◽  
Author(s):  
V.I. Alshits ◽  
D.M. Barnett ◽  
A.N. Darinskii ◽  
J. Lothe

1996 ◽  
pp. 409-412
Author(s):  
Shinsuke Hara ◽  
Takahiro Matsuda ◽  
Norihiko Morinaga

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