226,967 research outputs found
Line game-perfect graphs
The -edge colouring game is played with a set of colours on a
graph with initially uncoloured edges by two players, Alice (A) and Bob
(B). The players move alternately. Player has the first move.
. If , then only player may skip any move,
otherwise skipping is not allowed for any player. A move consists in colouring
an uncoloured edge with one of the colours such that adjacent edges have
distinct colours. When no more moves are possible, the game ends. If every edge
is coloured in the end, Alice wins; otherwise, Bob wins.
The -game chromatic index is the smallest
nonnegative integer such that Alice has a winning strategy for the
-edge colouring game played on with colours. The graph is
called line -perfect if, for any edge-induced subgraph of ,
where denotes the clique
number of the line graph of .
For each of the six possibilities , we
characterise line -perfect graphs by forbidden (edge-induced) subgraphs
and by explicit structural descriptions, respectively
Recommended from our members
Three-colourable perfect graphs without even pairs
AbstractWe still do not know how to construct the “most general” perfect graph, not even the most general three-colourable perfect graph. But constructing all perfect graphs with no even pairs seems easier, and here we make a start on it; we construct all three-connected three-colourable perfect graphs without even pairs and without clique cutsets. They are all either line graphs of bipartite graphs, or complements of such graphs
q-Coverings, codes, and line graphs
AbstractIn this paper we consider the relationship between q-coverings of a regular graph and perfect 1-codes in line graphs. An infinite class of perfect 1-codes in the line graphs L(Ik) is constructed
Line-graphs of cubic graphs are normal
A graph is called normal if its vertex set can be covered by cliques and also
by stable sets, such that every such clique and stable set have non-empty
intersection. This notion is due to Korner, who introduced the class of normal
graphs as an extension of the class of perfect graphs. Normality has also
relevance in information theory. Here we prove, that the line graphs of cubic
graphs are normal.Comment: 16 pages, 10 figure
The stable set polytope of claw-free graphs with stability number at least four. I. Fuzzy antihat graphs are W-perfect
Abstract Fuzzy antihat graphs are graphs obtained as 2-clique-bond compositions of fuzzy line graphs with three different types of three-cliqued graphs. By the decomposition theorem of Chudnovsky and Seymour [2] , fuzzy antihat graphs form a large subclass of claw-free, not quasi-line graphs with stability number at least four and with no 1-joins. A graph is W -perfect if its stable set polytope is described by: nonnegativity, rank, and lifted 5-wheel inequalities. By exploiting the polyhedral properties of the 2-clique-bond composition, we prove that fuzzy antihat graphs are W -perfect and we move a crucial step towards the solution of the longstanding open question of finding an explicit linear description of the stable set polytope of claw-free graphs
- …