Geodesic
Dismantlability Revisited for Ordered Sets and Graphs and the Fixed-Clique Property
Canadian mathematical bulletin, Tome 37 (1994) no. 4, pp. 473-481

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DOI

We give a unified treatment of several fixed-point type theorems by using the concept of dismantlability, extended from ordered sets to arbitrary graphs. For a graph G and a vertex x of G we let NG(X) denote the set of neighbours of x in G. We say that x is a subdominant vertex of G if there is a vertex y of G, distinct from x, such that NG(x)∪{x} ⊆ NG(y)∪{y}. If G has n vertices we say that G is dismantlable if the vertices of G can be listed as x1, x2, ..., xi,..., xn such that, for all i = 1,2,..., n— 1, xi is a subdominant vertex of the graph Gi = G — {xj : j < i}
DOI : 10.4153/CMB-1994-069-6
Mots-clés : 05C99, 06A10, graph, ordered set, subdominant vertex, dismantlable, graph homomorphism, fixedpoint, clique 
Ginsburg, John. Dismantlability Revisited for Ordered Sets and Graphs and the Fixed-Clique Property. Canadian mathematical bulletin, Tome 37 (1994) no. 4, pp. 473-481. doi: 10.4153/CMB-1994-069-6
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     title = {Dismantlability {Revisited} for {Ordered} {Sets} and {Graphs} and the {Fixed-Clique} {Property}},
     journal = {Canadian mathematical bulletin},
     pages = {473--481},
     year = {1994},
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     number = {4},
     doi = {10.4153/CMB-1994-069-6},
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