Peter Che Bor Lam

The 4-Choosability of Plane Graphs without 4-Cycles

A graphGis calledk-choosable ifkis a number such that if we give lists ofkcolors to each vertex ofGthere is a vertex coloring ofGwhere each vertex receives a color from its own list no matter what the lists are. In this paper, it is shown that each plane graph without 4-cycles is 4-choosable.

Some remarks on domination: SOME REMARKS ON DOMINATION

Proof: The proof is by induction on |V (G)| + |E(G)|. The smallest graph as described in the lemma is K1,3, for which the statement holds. This gives the start of our induction. Let x = |X| and y = |Y |. If there exists a vertex v in Y of degree at least 4, then delete any edge e incident to v. The subset A of G− e guaranteed by the inductive hypothesis is adjacent in G to every vertex in Y as desired. So we may assume that the vertices in Y are all of

Resonance Graphs and a Binary Coding for the 1-Factors of Benzenoid Systems

Applying the recently obtained distributive lattice structure on the set of 1-factors, we show that the resonance graphs of any benzenoid systems

On independent domination number of regular graphs

G

Orthogonal (g, f)-factorizations in networks

, as well as of general plane (weakly) elementary bipartite graphs, are median graphs and thus extend greatly Klavzar et al.s result. The

On incidence coloring for some cubic graphs

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A Distributive Lattice on the Set of Perfect Matchings of a Plane Bipartite Graph

-dimensional vectors of nonnegative integers as a labelling for the 1-factors of

Normal components, Kekulé patterns, and Clar patterns in plane bipartite graphs

G

L(j,k)- and circular L(j,k)-labellings for the products of complete graphs

with

The 3-choosability of plane graphs of girth 4

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