Search Results - "Hilton, A.J.W."

Hall's theorem and extending partial latinized rectangles by Goldwasser, J.L., Hilton, A.J.W., Hoffman, D.G., Özkan, Sibel

“…We generalize a theorem of M. Hall Jr., that an r×n Latin rectangle on n symbols can be extended to an n×n Latin square on the same n symbols. Let p, n,…”
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Degree-bounded factorizations of bipartite multigraphs and of pseudographs by Hilton, A.J.W.

“…For d ≥ 1 , s ≥ 0 a ( d , d + s ) - graph is a graph whose degrees all lie in the interval { d , d + 1 , … , d + s } . For r ≥ 1 , a ≥ 0 an ( r , r + a ) -…”
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A generalization of Talbot's theorem about King Arthur and his Knights of the Round Table by Hilton, A.J.W., Spencer, C.L.

“…Let G be a graph consisting of powers of disjoint cycles and let A be an intersecting family of independent r-sets of vertices. Provided that G satisfies a…”
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( r , r + 1 ) -factorizations of ( d , d + 1 ) -graphs by Hilton, A.J.W.

“…A ( d , d + 1 ) -graph is a graph whose vertices all have degrees in the set { d , d + 1 } . Such a graph is semiregular. An ( r , r + 1 ) -factorization of a…”
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Amalgamations of factorizations of complete equipartite graphs by Hilton, A.J.W, Johnson, Matthew

“…Let t be a positive integer, and let L=( l 1,…, l t ) and K=( k 1,…, k t ) be collections of nonnegative integers. A graph has a ( t, K, L) factorization if it…”
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Amalgamations of connected k-factorizations by Hilton, A.J.W, Johnson, Matthew, Rodger, C.A, Wantland, E.B

“…In this paper, necessary and sufficient conditions are found for a graph with exactly one amalgamated vertex to be the amalgamation of a k-factorization of K…”
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Relations among the fractional chromatic, choice, Hall, and Hall-condition numbers of simple graphs by Daneshgar, A., Hilton, A.J.W., Johnson Jr, P.D.

“…Hall's condition for the existence of a proper vertex list-multicoloring of a simple graph G has recently been used to define the fractional Hall and…”
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Aspects of edge list-colourings by Hilton, A.J.W., Slivnik, T., Stirling, D.S.G.

“…An assignment of colours to the edges of a multigraph is called an s -improper edge-colouring if no colour appears on more than s edges incident with any given…”
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The Overfull Conjecture and the Conformability Conjecture by Hilton, A.J.W., Holroyd, F.C., Zhao, Cheng

“…In this paper we show that under some fairly general conditions the Overfull Conjecture about the chromatic index of a graph G implies the Conformability…”
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Hamiltonian double latin squares by Hilton, A.J.W., Mays, M., Rodger, C.A., Nash-Williams, C.St.J.A.

“…A double latin square of order 2 n on symbols σ 1,…, σ n is a 2 n×2 n matrix A=( a ij ) in which each a ij is one of the symbols σ 1,…, σ n and each σ k occurs…”
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Non-conformable subgraphs of non-conformable graphs by Hilton, A.J.W., Hind, H.R.

“…We show that if G and H are non-conformable graphs, with H being a subgraph of G of the same maximum degree Δ( G), and if Δ(G)⩾⌈ 1 2 |V(G)|⌉ , then | V( H)|=|…”
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The structure of totally critical graphs of odd order by Dugdale, J.K, Hilton, A.J.W

“…It has been known for some time that if the Conformability Conjecture is true, then we can say exactly which graphs G of maximum degree Δ(G)⩾ 1 2 |V(G)| and…”
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At most k-to-1 mappings between graphs, II by Heath, Jo, Hilton, A.J.W.

“…Suppose that f is a (⩽ k)-to-1 function from a vertex set of a graph G onto a vertex set of a graph H. We ask when f extends to a continuous (⩽ k)-to-1 map…”
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The Hall number, the Hall index, and the total Hall number of a graph by Hilton, A.J.W, Johnson, P.D

“…We discuss the relationship between the Hall number of a graph and other well-known graph parameters, including the choice number and the chromatic number. We…”
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Vertex-splitting and chromatic index critical graphs by Hilton, A.J.W., Zhao, C.

“…We study graphs which are critical with respect to the chromatic index. We relate these to the Overfull Conjecture and we study in particular their…”
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Fractional latin squares, simplex algebras, and generalized quotients by Dugdale, J.K., Hilton, A.J.W., Wojciechowski, J.

“…Recently the authors defined the concept of a weighted quasigroup, and showed that each weighted quasigroup is the amalgamation of a quasigroup. Similar…”
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A Vertex-Splitting Lemma, de Werra's Theorem, and Improper List Colourings by Hilton, A.J.W., Stirling, D.S.G., Slivnik, T.

“…We prove a new vertex-splitting lemma which states that if a multigraphGhas maximum multiplicity of at mostp, then each vertex u can be split into ⌈(d(u)/p)⌉…”
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Triangulations of 3-way regular tripartite graphs of degree 4, with applications to orthogonal latin squares by Andersen, L.D., Hilton, A.J.W.

“…If G is a regular tripartite graph of degree d( G) with tripartition ( A, B, C) of V( G) such that the bipartite subgraphs induced by each of A ∪ B, B ∪ C, C ∪…”
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Totally Critical Even Order Graphs by Hamilton, G.M., Hilton, A.J.W., Hind, H.R.F.

“…A graph is totally critical if it is Type 2, connected, and the removal of any edge reduces the total chromatic number. A good characterization of all totally…”
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Graphs that admit 3-to-1 or 2-to-1 maps onto the circle by Hilton, A.J.W., Liu, J.P., Zhao, C.

“…We give a complete and explicit characterization of the connected graphs which admit a continuous 3-to-l map onto the circle, and of the connected graphs which…”
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