Results 51 to 60 of about 406 (81)
, 2012 2010 Mathematics Subject Classification: Primary 05C25. Secondary 20K01, 05C45.Let Cay(G;S) denote the Cayley graph on a finite group G with connection set S. We extend two results about the existence of cycles in Cay(G;S) from cyclic groups to arbitrary
Parmenter, M. M.
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Dirac type condition and Hamiltonian graphs [PDF]
, 2011 2010 Mathematics Subject Classification: 05C38, 05C45.In 1952, Dirac introduced the degree type condition and proved that if G is a connected graph of order n і 3 such that its minimum degree satisfies d(G) і n/2, then G is Hamiltonian.
Zhao, Kewen
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Eulerian $k$-dominating reconfiguration graphs [PDF]
Discrete Mathematics & Theoretical Computer ScienceFor a graph $G$, the vertices of the $k$-dominating graph, denoted $\mathcal{D}_k(G)$, correspond to the dominating sets of $G$ with cardinality at most $k$. Two vertices of $\mathcal{D}_k(G)$ are adjacent if and only if the corresponding dominating sets
M. E. Messinger, A. Porter
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Hamilton cycles in almost distance-hereditary graphs [PDF]
, 2013 Let $G$ be a graph on $n\geq 3$ vertices. A graph $G$ is almost distance-hereditary if each connected induced subgraph $H$ of $G$ has the property $d_{H}(x,y)\leq d_{G}(x,y)+1$ for any pair of vertices $x,y\in V(H)$.
Chen, Bing, Ning, Bo
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ALTERNATING AND SYMMETRIC GROUPS WITH EULERIAN GENERATING GRAPH
Forum of Mathematics, Sigma, 2017 Given a finite group $G$ , the generating graph $\unicode[STIX]{x1D6E4}(G)$
ANDREA LUCCHINI, CLAUDE MARION
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On factors of 4-connected claw-free graphs [PDF]
, 1999 We consider the existence of several different kinds of factors in 4-connected claw-free graphs. This is motivated by the following two conjectures which are in fact equivalent by a recent result of the third author.
Broersma, H.J. +2 more
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Cycle Partitions in Dense Regular Digraphs and Oriented Graphs
Forum of Mathematics, SigmaA conjecture of Jackson from 1981 states that every d-regular oriented graph on n vertices with $n\leq 4d+1$ is Hamiltonian. We prove this conjecture for sufficiently large n.
Allan Lo +2 more
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Rainbow Hamilton cycles in random regular graphs
, 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 ...
Janson, Svante, Wormald, Nicholas
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Eulerian character degree graphs of solvable groups
AKCE International Journal of Graphs and CombinatoricsLet G be a finite group, let Irr(G) be the set of all complex irreducible characters of G and let cd(G) be the set of all degrees of characters in [Formula: see text] Let [Formula: see text] be the set of all primes that divide some degrees in [Formula ...
G. Sivanesan +2 more
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Expansion of gene clusters, circular orders, and the shortest Hamiltonian path problem. [PDF]
J Math Biol, 2018 Prohaska SJ +7 more
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