Results 11 to 20 of about 445,337 (327)
Fast strategies in biased Maker--Breaker games [PDF]
Discrete Mathematics & Theoretical Computer Science, 2018 We study the biased $(1:b)$ Maker--Breaker positional games, played on the edge set of the complete graph on $n$ vertices, $K_n$. Given Breaker's bias $b$, possibly depending on $n$, we determine the bounds for the minimal number of moves, depending on ...
Mirjana Mikalački, Miloš Stojaković
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Hamilton cycles in quasirandom hypergraphs [PDF]
Random Structures & Algorithms, 2016 We show that, for a natural notion of quasirandomness in $k$-uniform hypergraphs, any quasirandom $k$-uniform hypergraph on $n$ vertices with constant edge density and minimum vertex degree $ (n^{k-1})$ contains a loose Hamilton cycle. We also give a construction to show that a $k$-uniform hypergraph satisfying these conditions need not contain a ...
Lenz, John +2 more
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Powers of Hamilton cycles in pseudorandom graphs [PDF]
, 2014 We study the appearance of powers of Hamilton cycles in pseudorandom graphs, using the following comparatively weak pseudorandomness notion. A graph $G$ is $(\varepsilon,p,k,\ell)$-pseudorandom if for all disjoint $X$ and $Y\subset V(G)$ with $|X|\ge ...
Peter Allen +4 more
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Rainbow Hamilton cycles in random regular graphs [PDF]
, 2005 A rainbow subgraph of an edge-coloured graph has all edges of distinct colours. A random d-regular graph with d even, and having edges coloured randomly with d/2 of each of n colours, has a rainbow Hamilton cycle with probability tending to 1 as n tends ...
Svante Janson, Nicholas Wormald
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Hamilton cycles in graphs and hypergraphs: an extremal perspective [PDF]
, 2014 As one of the most fundamental and well-known NP-complete problems, the Hamilton cycle problem has been the subject of intensive research. Recent developments in the area have highlighted the crucial role played by the notions of expansion and quasi ...
Daniela Kühn, Deryk Osthus
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Finding Hamilton cycles in random intersection graphs [PDF]
Discrete Mathematics & Theoretical Computer Science, 2018 The construction of the random intersection graph model is based on a random family of sets. Such structures, which are derived from intersections of sets, appear in a natural manner in many applications. In this article we study the problem of finding a
Katarzyna Rybarczyk
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Identifying Hamilton cycles in the Cartesian product of directed cycles
AKCE International Journal of Graphs and Combinatorics, 2020 Let be a Cartesian product of directed cycles. It is known that has a Hamilton cycle if there is a permutation of that satisfies and for some positive integers , where . In addition, if then has two arc-disjoint Hamilton cycles.
Zbigniew R. Bogdanowicz
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On Implicit Heavy Subgraphs and Hamiltonicity of 2-Connected Graphs
Discussiones Mathematicae Graph Theory, 2021 A graph G of order n is implicit claw-heavy if in every induced copy of K1,3 in G there are two non-adjacent vertices with sum of their implicit degrees at least n. We study various implicit degree conditions (including, but not limiting to, Ore- and Fan-
Zheng Wei, Wideł Wojciech, Wang Ligong
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Well-spread sequences and edge-labellings with constant Hamilton-weight [PDF]
Discrete Mathematics & Theoretical Computer Science, 2004 A sequence (a_i) of integers is \emphwell-spread if the sums a_i+a_j, for ...
Peter Mark Kayll
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Difference divisor graph of the finite group [PDF]
International Journal of Research in Industrial Engineering, 2018 Let (Zn, +) be a finite group of integers modulo n and Dn a non-empty subset of Zn containing proper devisors of n. In this paper, we have introduced the difference divisor graph Diff (Zn, Dn) associated with Zn whose vertices coincide with Zn such that ...
R. V M S S Kiran Kumar, T. Chalapathi
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