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pro vyhledávání: '"Kayll, P. Mark"'
Autor:
Kayll, P. Mark, Morris, Michael
We prove that for every oriented graph $D$ and every choice of positive integers $k$ and $\ell$, there exists an oriented graph $D^*$ along with a surjective homomorphism $\psi\colon V(D^*) \to V(D)$ such that: (i) girth$(D^*) \geq\ell$; (ii) for eve
Externí odkaz:
http://arxiv.org/abs/2307.09461
We introduce, and partially resolve, a conjecture that brings a three-centuries-old derangements phenomenon and its much younger two-decades-old analogue under the same umbrella. Through a graph-theoretic lens, a derangement is a perfect matching in
Externí odkaz:
http://arxiv.org/abs/2209.11319
Autor:
Kayll, P. Mark, Larson, Craig E.
We leverage an algorithm of Deming [R.W. Deming, Independence numbers of graphs -- an extension of the Koenig-Egervary theorem, Discrete Math., 27(1979), no. 1, 23--33; MR534950] to decompose a matchable graph into subgraphs with a precise structure:
Externí odkaz:
http://arxiv.org/abs/2205.10598
Autor:
Parsa, Esmaeil, Kayll, P. Mark
Publikováno v:
Australasian Journal of Combinatorics, Volume 79(3) (2021), Pages 371-379
An acyclic homomorphism of a digraph $C$ to a digraph $D$ is a function $\rho\colon V(C)\to V(D)$ such that for every arc $uv$ of $C$, either $\rho(u)=\rho(v)$, or $\rho(u)\rho(v)$ is an arc of $D$ and for every vertex $v\in V(D)$, the subdigraph of
Externí odkaz:
http://arxiv.org/abs/2101.09751
Autor:
Kayll, P. Mark, Perkins, Dave
We continue our studies of burn-off chip-firing games from [Discrete Math. Theor. Comput. Sci. 15 (2013), no. 1, 121-132; MR3040546] and [Australas. J. Combin. 68 (2017), no. 3, 330-345; MR3656659]. The latter article introduced randomness by choosin
Externí odkaz:
http://arxiv.org/abs/2007.09732
Autor:
Kayll, P. Mark, Parsa, Esmaeil
We prove that for every digraph $D$ and every choice of positive integers $k$, $\ell$ there exists a digraph $D^*$ with girth at least $\ell$ together with a surjective acyclic homomorphism $\psi\colon D^*\to D$ such that: (i) for every digraph $C$ o
Externí odkaz:
http://arxiv.org/abs/2007.01981
Akademický článek
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Publikováno v:
Can. J. Math.-J. Can. Math. 64 (2012) 1310-1328
Let C and D be digraphs. A mapping $f:V(D)\to V(C)$ is a C-colouring if for every arc $uv$ of D, either $f(u)f(v)$ is an arc of C or $f(u)=f(v)$, and the preimage of every vertex of C induces an acyclic subdigraph in D. We say that D is C-colourable
Externí odkaz:
http://arxiv.org/abs/1109.5208
Akademický článek
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