AbstractWe discuss the following conjecture: If G = (V, E) is a Δ-regular simple graph with an even number of vertices at most 2Δ then G is Δ edge colorable.In this paper we show that the conjecture is true for large graphs if | V | < (2 − ε)Δ. We discuss the related results
AbstractFor large values of Δ, it is shown that all Δ-regular finite simple graphs possess a non-tri...
AbstractSuppose every vertex of a graph G has degree k or k + 1 and at least one vertex has degree k...
AbstractIt was conjectured by Kronk and Mitchem in 1973 that simple plane graphs of maximum degree Δ...
AbstractWe discuss the following conjecture: If G = (V, E) is a Δ-regular simple graph with an even ...
AbstractChetwynd and Hilton have elsewhere posed two conjectures, one a general statement on edge-co...
AbstractWe consider the following conjecture:Let G be a k-regular simple graph with an even number n...
AbstractFor any simple graph G, Vizing's Theorem [5] implies that Δ(G) ⩽ χ(G) ⩽ Δ(G) + 1, where Δ(G)...
AbstractIn this note we summarize some of the progress made recently by the author, A.G. Chetwynd an...
AbstractLet f(k) be the largest number such that each k-regular bipartite graph with 2n vertices has...
AbstractThe total chromatic number ξT(G) of a graph G is the least number of colours needed to colou...
AbstractWe show that there exists a family of r-regular graphs of arbitrarily large excessive index ...
AbstractThe vertex-distinguishing index χs′(G) of a graph G is the minimum number of colours require...
AbstractThe Δ-subgraph GΔ of a simple graph G is the subgraph of G induced by the vertices of maximu...
AbstractLet G be a d-regular simple graph with n vertices. Here it is proved that for d > n−1, G con...
AbstractWe show that a regular graph G of order at least 6 whose complement Ḡ is bipartite has total...
AbstractFor large values of Δ, it is shown that all Δ-regular finite simple graphs possess a non-tri...
AbstractSuppose every vertex of a graph G has degree k or k + 1 and at least one vertex has degree k...
AbstractIt was conjectured by Kronk and Mitchem in 1973 that simple plane graphs of maximum degree Δ...
AbstractWe discuss the following conjecture: If G = (V, E) is a Δ-regular simple graph with an even ...
AbstractChetwynd and Hilton have elsewhere posed two conjectures, one a general statement on edge-co...
AbstractWe consider the following conjecture:Let G be a k-regular simple graph with an even number n...
AbstractFor any simple graph G, Vizing's Theorem [5] implies that Δ(G) ⩽ χ(G) ⩽ Δ(G) + 1, where Δ(G)...
AbstractIn this note we summarize some of the progress made recently by the author, A.G. Chetwynd an...
AbstractLet f(k) be the largest number such that each k-regular bipartite graph with 2n vertices has...
AbstractThe total chromatic number ξT(G) of a graph G is the least number of colours needed to colou...
AbstractWe show that there exists a family of r-regular graphs of arbitrarily large excessive index ...
AbstractThe vertex-distinguishing index χs′(G) of a graph G is the minimum number of colours require...
AbstractThe Δ-subgraph GΔ of a simple graph G is the subgraph of G induced by the vertices of maximu...
AbstractLet G be a d-regular simple graph with n vertices. Here it is proved that for d > n−1, G con...
AbstractWe show that a regular graph G of order at least 6 whose complement Ḡ is bipartite has total...
AbstractFor large values of Δ, it is shown that all Δ-regular finite simple graphs possess a non-tri...
AbstractSuppose every vertex of a graph G has degree k or k + 1 and at least one vertex has degree k...
AbstractIt was conjectured by Kronk and Mitchem in 1973 that simple plane graphs of maximum degree Δ...
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